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Author:
L. Aleksidze
 
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2010 Mathematics Subject Classification Index
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E-martingales
O-exponential tail
q variation
Q∞-expansion
X-martingales
α-stable like process
α-stable process
Ξ-coalescent
σ-martingale
φ-sub-Gaussian processes
11B37
28A50
28C20
33C15
34L10
47A10
47D07
60A10
60B10
60C05
60E05
60E10
60F05
60F10
60F15
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60G44
60G50
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60G60
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60J80
60J90
60K05
62F40
62G10
62M10
91A05
91A15
91B05
91B70
91G05
91G20
92D15
Additive odds model
AIC and BIC criteria
allocation principle
almost sure central limit theorem
American options
Anomalous diffusion
Anomalous diffusions
approximation
approximation rate
AR(1) representation
AR(1)-characterisation
asymptotic behavior
asymptotic behavior of additive functionals
asymptotic behavior of functionals
asymptotic consistency
asymptotic covariance matrix estimation
asymptotic distribution
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Asymptotic geometric analysis
asymptotic mean square quasistability
Asymptotic normality
Asymptotic normality of estimators
Asymptotic theory
asymptotically independent estimators
asymptotics
attributable proportion
autoregressive model
autoregressive models
Averaging principle
Backward stochastic differential equation
Bahadur Ranga Rao
Banach lattices
BDG inequalities
Berkson model
Bernstein function
Bernstein inequality
Berry–Esséen bound
Berry–Essen bounds
Besov space
Bessel functions
Bessel process
Bessel transforms
Beta distribution
Beta random variable
Bi-risk model
Bi-seasonal model
bias reduction
bifractional brownian motion
BINAR
binary experiments
binary regression
binomial distribution
birth–death Markov chain
Bismut–Elworthy–Li formula
blind source separation
Bonus–malus system
boundary effect
bounded in the mean solution
Branching process
Brownian motion
BSDE and reflected BSDE
BSDEs
Cannings model
CARMA processes
case-control data
causality
Central limit theorem
Chacon–Walsh construction
change of measures
change of time
Chaos expansion
characteristic function
Chirp signal
circle homeomorphisms
claim type
classical measurement error
Clayton copula
Cliquet option pricing
closure property
coalescent with dust
cointegrated sequences
cointegration
combinatorial approach
compact operator
comparison theorem
compensator
Complete market
complete monotonocity
Compound mixed renewal process
compound Poisson process
Compound Poisson process of order k
compound Poisson-Gamma subordinator
Compound renewal process
computation of greeks
concentration bounds
concentration function
concentration inequalities
Conditional expectations
conditional maximum likelihood estimators
conditional processes
Conditionally Gaussian processes
Conditioning to stay positive
confidence ellipsoid
confidence interval
confidence region
conic intrinsic volumes
Conic section fitting
consistency
Consistent criteria
consistent estimator
consistent estimator of best prediction
consistent estimators
Consistently varying distribution
consistently varying tail
constant dividend strategy
constrained optimization
continuous additive functional
continuous time
Continuous-time nonlinear regression
contraction and semicontraction principles
convergence
convertible features
convex stochastic order
convex stochastic process
convexity
convolution closure
copula
Corrected Maximum Likelihood Estimator
correlogram
Count data
Coupling
coupon collector’s problem
covariance
covariance function
covariance functions
covariance matrix
Cox proportional hazards model
Cox–Ingersoll–Ross process
Cramér–Lundberg risk model
Cramér’s theorem
criterion for testing hypotheses
curve fitting
cylindrical random variable
De Vylder approximation
Decompounding
dense set of distributions
density functions
Dependence measure
dependent claims
deviation inequalities
Difference equation
Difference equations
Diffusion-type processes
digital option
directional extremes
discrete and distributed delays
discrete approximation
discrete approximation scheme
Discrete chaos
Discrete distribution
discrete random fields
discrete time
discrete time risk model
discrete-time approximations
discretized model
distance covariance
distributed delay
distribution function
distribution of local time
distribution of sumpremum
distribution of sumpremum of solution
divergence form
Donsker theorem
Doob–Meyer decomposition
drift parameter
drift parameter estimation
drifted Brownian motion
Econometrics time series
eigenfunction
eigenspace
eigenvalue
EM-algorithm
empirical means
entire asymptotic separation
Entropic Value-at-Risk
entropy
entropy methods
entropy power inequality
equilibrium control
equity indexed annuity
Equivalence in law
ergodic process
ergodic theorem
Erlang mixture distribution
errors in variables
errors-in-variables model
estimation
estimator
estimator moments
estimator of baseline hazards function
estimators of offspring mean
Euler–Maruyama scheme
Euler–Poisson–Darboux equation
exact marginal probability distribution
exchangeability
exchangeable coalescent
excursion probability
existence and uniqueness of the solution to SDE
existence, uniqueness, weak probabilistic solution
exit problems
expansion of odds ratios
expected discounted dividend payments
expected maximum
exponential bound
Exponential distribution
exponential functional
exponential mean square stability
exponential moment
exponential moments and potentials
exponential tail
exponential tightness
external angles
extinction
extinction probability
Extreme values
factorial moments
fair option price
faithful Vitali coverings
faithfulness of fine packing system for packing dimension calculation
Farlie–Gumbel–Morgenstern copula
Fejèr sums
Feynman-Kac formula
Feynman–Kac semigroup
FGM copula
Filtration
Financial markets
Finite mixture model
finite speed of propagation
finite time survival probability
finite-time ruin probability
Fisher information inequality
Fixed-point equation
Fluctuation theory in discrete time
forward rate
forward recurrence time
Fourier transform
fourth moment theorems
fractality
fractals
fractional advection-dispersion
fractional Brownian motion
fractional Brownian sheet
fractional calculus
Fractional counting processes
Fractional Cox–Ingersoll–Ross process
fractional diffusion
Fractional equations
fractional gradient
fractional integral
fractional Laplacian
Fractional Lévy process
Fractional Ornstein–Uhlenbeck processes
fractional Poisson process
fractional process
fractional processes
fractional Vasicek model
fractionality
Fractionally integrated inverse stable subordinators
Frank copula
Fresnel integrals
functional limit theorem
functional limit theorems
functional model
functional moments
functional Γ-calculus
fundamental solution
gain–loss ratio
game options
gamma distribution
gamma function
Gamma mixing
Gamma subordinator
Gamma-type process
Gärtner–Ellis condition
Gauss hypergeometric
Gauss hypergeometric function
Gaussian distribution
Gaussian process
Gaussian processes
Gaussian random field
Gaussian second-order moving average model
Gaussian sheets
Gaussian Volterra noise
Gaussian Volterra process
Gaussian Volterra processes
Gaussian-Volterra process
general stochastic measure
Generalized backward stochastic differential equations (GBSDEs) with jumps
Generalized BSDE with jumps
Generalized BSDEs with jumps
generalized counting process
generalized estimating equations
Generalized fractional and subfractional Brownian motion
generalized fractional derivatives
generalized integer-valued autoregressive processes
Generalized log-Pareto distribution
generalized solution
generalized Wright function
generated σ-field
generating functions
geometric reproduction branching process
Gerber–Shiu function
Gibbs inequality
global solution
Goodness-of-fit test
Granger causality
graphical representation
Greeks
Green’s function
Hahn and Jordan decompositions
harmonic numbers
harmonizable processes
Hausdorff saturation
Hausdorff–Besicovitch dimension
Hausdorff–Besicovitch dimension of a set
Heat equation
Heavy tail
Heavy-tailed distribution
heavy-tailed particle tracking
Hellinger distance
Hermite–Hadamard inequality
heteroscedastic measurement errors
high frequency data
High-dimensional asymptotics
high-dimensional convexity
high-order moments
Higher-order dispersive equations
hitting times
Hölder continuity
Hölder regularity
homogeneous and isotropic strongly dependent Gaussian random field
Homogeneous transient diffusion process
Hurst index estimation
hybrid stochastic volatility models
hypergeometric function
hypothesis testing
increasing path
Increasing process
independent complements
Independent indicators
indifference principle
Inference for mixtures
Infinite divisibility
infinite occupancy
infinite particle systems
infinite-dimensional stochastic differential equations
Infinitely divisible logarithmic series distribution
Infinitely divisible random measure
inhomogeneity
inhomogeneous distributions
inhomogeneous Markov chain
Inhomogeneous model
initial random population
initial values
instant enforcement
insurance model
integral equation with weakly singular kernel
integral functional
integral representation
integral-partial differential equations
integrated distribution functions
integrated quantile functions
integro-differential equation
Interacting Brownian motions
interacting particles
interaction of risk factors
internal angles
intersection of σ-fields
intersection volume
inverse Gaussian distribution
inverse of stable subordinator
inverse subordinator
inverse subordinators
inversion of the Volterra representation
irregular barrier
iterated function systems
iterated log-type law
Itô formula
Itô’s isometry
jackknife
joint asymptotic distribution
jointly strictly sub-Gaussian noise
jump-diffusion model
jump-diffusion process
Kato class
Kies distribution
Kolmogorov metric
Kolmogorov norm
Kolmogorov-type equation
Ky-Fan inequality
ℓpn-balls
ℓpn-spheres
Lp solution
Lagrange inversion
Lambert function
Lambert-W function
Lambert-W functions
LAN property
Laplace distribution
Laplace transform
Laplace–Beltrami operators
large deviation principles
Large deviations
large deviations principle
large financial market
Lattice of complete σ-fields
law of the iterated logarithm
Least common multiple
least favorable spectral density
least squares estimate
least squares estimate in the Walker–Brillinger sense
least squares estimator
LePage series
Leslie–Gower and Holling-type II functional response
Lévy density
Lévy distribution
Lévy driven SDE
Lévy process
Lévy process; moving average
Lévy processes
Lévy white noise
Lévy-type processes
Lieb’s splitting inequality
likelihood function
limit theorem
limit theorems
Linear errors-in-variables model
linear operator
Linear price impact
Linear regression
local alternatives
local behavior
local martingale
local mixing
local norm
Local time
locally perturbed random walks
log-return of financial asset
log-Sobolev inequality
logarithmic Sobolev inequalities
Logistic regression
long-range dependence
long-range dependency
LQ control problem
Lundberg-type inequality
Lundberg’s inequality
machine learning
Malliavin calculus
Malliavin–Stein approach for normal approximations
Marked point process
market-consistent calibration
Markov Binomial distribution
Markov chain
Markov chains
Markov generator
Markov process
Markov processes
Markov renewal process
Markov triple
Markovity
Martingale
martingale characterization
martingale measures
martingales
maximal residual
maximum likelihood
maximum likelihood estimation
maximum likelihood estimator
mean square error
measurement error model
measurement errors
Meixner distribution
Meixner–Lévy process
Mertens decomposition
Metatime
method of majorizing measures
method of moments
metric theory of ROE
mild solution
min- and max-distributions
minimal
minimal clade
minimax estimator
Minimax identity
minimax-robust estimate
minimax-robust spectral characteristic
minimum distance
Mittag-Leffler function
Mittag-Leffler functions
mixed fractional Brownian motion
mixed model
mixed normal distribution
mixed Poisson processes
mixture of tempered stable subordinators
mixture of the classical and Berkson errors
mixture with varying concentrations
model-based clustering
Model-free approach in Mathematical Finance
moderate deviations
moderate deviations principle
modified geometric fractional Ornstein-Uhlenbeck process
modified geometric Ornstein-Uhlenbeck process
moment asymptotics
moment generating function
moment inequalities
moments
monotone generator
Monte Carlo method
Monte Carlo simulations
Moore–Penrose inverse
moving averages
multi-factor model
multi-layer dividend strategy
multi-mixed fractional Brownian motion
multi-mixed fractional Ornstein–Uhlenbeck process
Multi-seasonal discrete-time risk model
multidimensional compound Poisson process
multiparameter Gaussian processes
multiple integral
multiple Wiener integrals
multiple Wiener–Itô integrals
multiplicative perturbed random walk
Multitype Galton–Watson branching processes with immigration
multivariable Haar functions
multivariate analysis
multivariate errors-in-variables model
multivariate regression
Multivariate trigonometric model
N-self-similar sets
nearest neighbor search
negative binomial distribution
negative definite function
net profit condition
neural networks
non-ergodic process
non-Gaussian limit theorem
non-Gaussian process
non-Lipschitz coefficients
Non-monotonic functions
non-proportional hazards
non-uniform estimate
noncentral limit theorems
nonconcave utility
nonlinear diffusion equation
nonlinear regression
Nonlinear regression model
Nonlinear stochastic differential equation
nonlocal equations
nonnegative stationary processes
nonparametric Bayesian estimation
nonparametric estimation
Nonparametric regression
nonpersistence
nonpersistence in the mean
nonregular dependence on the parameter
normal inverse Gaussian distribution
number of renewals
numerical approximation
numerical methods
Objective option price
occupancy problem
occupation time
occupation-time option
one-step analysis
optimal liquidation
optimal strategies
Optimal value of absolute constant in Berry–Esseen inequality
option pricing
order of nonlinearity higher than one
order statistics property
ordinary least squares
Orlicz process
Orlicz space
Ornstein–Uhlenbeck process
orthogonal
orthogonal regression
outer measure
Packing dimension of a set
packing-dimension-preserving transformations
parameter estimation
partial Bell polynomials
partial differential equation
path-dependent exotic option
path-dependent stochastic differential equations
pathwise Stratonovich integral
periodogram
permanent insurance policy
persistence diagram
persistent Betti number
perturbation
piecewise constant coefficients
piecewise integro-differential equation
Poincaré–Borel lemma
Poisson
Poisson distribution
Poisson measure
Poisson point process
Poisson process
Poisson space
Poisson-Gamma subordinator
polygonal approximation
polyhedral cones
polynomial errors-in-variables model
post-crisis model
posterior contraction rate
potential measures
power of test
precise large deviations
predictable representation property
Prediction
preferential attachment
premium calculation principle
premium relativity
pricing
prime counts
principal components
probabilistic analysis
probabilities of large deviations
probability
probability measure change
probability metrics
probability of bankruptcy
Process with independent increments
processes with finite variation
progressively equivalent (martingale) measures
progressively equivalent measures
projection problem
proximity of solutions
pseudo-gradient
pseudo-process
purely nondeterministic random fields
Q̃-expansion of real numbers
Q*-expansion
quadratic variation
Quantile functions
Quantitative functional central limit theorem
quasi-helix property
queuing systems
random closed set
random coefficients
random convolution
random convolution closure
random dynamical systems
random environment
Random fields
Random flights
random graph
random initial conditions
random matrices
random measure
random process with immigration
random sum
random topology
random tree
Random variables with independent GLS-symbols
random velocity
random walk
random walk in a strip
random walk with barriers
random walks and bridges
randomized periodogram
randomly stopped maximum
randomly stopped maximum of sums
randomly stopped sum
Rate of convergence
rate of growth
rates of convergence
rates of weighted entropy and information
rcll barrier
RCLL martingale
real harmonizable fractional stable process
recurrence sequences
recursive calculation
recursive formula
Reflected backward doubly stochastic differential equations
reflected BSDE
reflexive generalized inverse
regenerative processes
regions of stability
regression calibration model
regular conditional probabilities
regular statistical experiment
regularly varying distribution
regularly varying function
relative entropy
remaining term
renewal model
Renewal process
renewal theory
Rényi entropy
replacement model for random lifetimes
representation of Gaussian processes
residual correlogram
Restricted Oppenheim expansion
Riemann zeta function
right censored data
right censoring
risk measure
Risk model
Risk model with stochastic premiums
risk process
robust utility functionals
ruin probability
ruin problem
ruin theory
run-and-tumble models
Running maximum
sample path differentiability
Sampled extrema
sandwiched process
scale free
SDEs
SDEs with distributional drift
second Wiener chaos
Second-order Galton–Watson process with immigration
Selberg theorem
self-normalized sums
Self-similar random field
Semi-Markov chain
semimartingality
semiparametric estimation
sensitivity analysis
series expansions
Set indexed process
sharp asymptotics
sharp large deviations
Short rate
short-range dependence
shortfall risk
shot noise process
Signed compound Poisson approximation
signed measures
similarity search
simulation
simultaneous estimation of baseline hazard rate and regression parameter
simultaneous multiple collisions
singular
Singular covariance matrix
singular inverse Wishart
singular probability distributions
Singular Wishart distribution
singularly continuous probability measures
Skellam process
skew Bessel process
small counts
small deviation
smoothness of the density
space-time white noise
Sparre Andersen identity
Spatial birth-and-death processes
spectrum
sphere
spherical Brownian motion
spherical harmonics
Square Gaussian stochastic process
stability in probability
stable convergence
Stable Lévy Diffusion
stable Lévy processes
stable random measure
stationarity
stationary distribution
stationary distributions
stationary Gaussian noise
stationary Gaussian stochastic process
stationary process
stationary processes
stationary random field
stationary random fields
stationary solution
stationary-increment processes
Stein-Malliavin calculus
Stein’s method
Stirling numbers
Stochastic Burgers equation
stochastic cable equation
stochastic delay differential equations
Stochastic differential equation
Stochastic differential equations
stochastic equation
stochastic Fourier series
stochastic fractional integrals
Stochastic geometry
stochastic heat equation
stochastic independence
stochastic integral
stochastic linear growth condition
Stochastic Lipschitz coefficient
stochastic Lipschitz condition
Stochastic Lotka–Volterra mutualism model
Stochastic maximum principle
Stochastic measure
Stochastic modified-Leray-alpha model
stochastic monotone coefficient
Stochastic mutualism model
stochastic nonstationarity
stochastic optimal control
stochastic parabolic equation
Stochastic partial differential equation
stochastic partial differential equations
stochastic permanence
stochastic perturbations
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Stochastic sequence with stationary increments
Stochastic transport equation
stochastic ultimate boundedness
stochastic volatility
stochastic Volterra equations
stochastic wave equation
stopping time
Stratonovich integral
strictly stationary processes
strong approximation
strong asymptotic arbitrage
strong consistency
strong large deviations
strong laws of large numbers
strong limit theorem
strong persistence in the mean
strongly separable probability measures
structured product
Sub-fractional Ornstein–Uhlenbeck process of second kind
sub-Gaussian processes
Sub-Gaussian random processes
subordinator
subordinators
subspace clustering
Sums of Gaussian squares
supremum distribution
supremum of sums
survival probability
SVV model
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symbolic algebra
symmetric integral
synchronization
tail behavior
tail probability
Tangency portfolio
tapered data
Taylor’s power law
Telegraph equation with time-dependent velocity
telegraph process
Tempered fractional derivatives
tempered stable subordinator
temporal and contemporaneous aggregation
temporary insurance policy
terminal joint distribution
the Feret diameter
three-seasonal model
threshold strategy
Time-change
time-fractional Poisson process
time-inconsistency
total least squares
total least squares estimator
total variation norm
trajectories of random functions
transition matrix
Transition probability density
trawl process
trends and breaks
trimmed filtration
trimmed regions
truncated pseudomoments
ultimate ruin probability
ultimate time survival probability
uniqueness of a solution
upwards skip-free killed random walks
utility maximization
vantage point tree
Variance Gamma process
variance-gamma process
variational distance
variational inequality
varying coefficients
varying deductible
viscosity solution
Volterra type Gaussian processes
volume of convex bodies
von-Mises type parameterization
vp-tree
wave equation
weak and strong solutions
weak approximation rates
weak convergence
weak convergence method
weak persistence in the mean
weak solution
weakly separable
Weibull distribution
Weighted entropy
Weighted fractional Vasicek model
weighted premium
weighted random variables
Weyl chambers
Wiener space
Wiener-chaos expansions
Wiener–Itô integral
Workshop
Wright
Yosida approximation
Young integral
Yule model
zero-coupon bond
Zonotopes
Φ-Sobolev inequalities
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JEL — D52
JEL — G12
JEL — G22
MSC2010 — 01-06
MSC2010 — 05-08
MSC2010 — 05C80
MSC2010 — 11A05
MSC2010 — 11B73
MSC2010 — 11K55
MSC2010 — 11K65
MSC2010 — 11N60
MSC2010 — 15A52
MSC2010 — 1M06
MSC2010 — 26A30
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MSC2010 — 26A48
MSC2010 — 26A51
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MSC2010 — 28A80
MSC2010 — 28E05
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MSC2010 — 33E99
MSC2010 — 34A08
MSC2010 — 34F05
MSC2010 — 34G20
MSC2010 — 34K20
MSC2010 — 34K50
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The consistent criteria of hypotheses
L. Aleksidze
M. Mumladze
Z. Zerakidze
https://doi.org/10.15559/vmsta-2014.1.1.5
Pub. online:
27 Jun 2014
Type:
Research Article
Open Access
Journal:
Modern Stochastics: Theory and Applications
Volume 1, Issue 1 (2014), pp. 3–11
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Abstract
In this paper we define the consistent criteria of hypotheses such as the probability of any kind of errors is zero for given criteria. We prove necessary and sufficient conditions for the existence of such criteria.
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