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E-martingales
nth-order fractional Brownian motion
O-exponential tail
q variation
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α-stable like process
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Additive odds model
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American options
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Averaging principle
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Banach lattices
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Chaos expansion
characteristic function
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claim type
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Cliquet option pricing
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Complete market
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Compound mixed renewal process
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conic intrinsic volumes
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constant dividend strategy
constrained optimization
continuous additive functional
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contraction and semicontraction principles
convergence
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convex stochastic order
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copula
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Count data
Coupling
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covariance
covariance function
covariance functions
covariance matrix
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criterion for testing hypotheses
curve fitting
cylindrical random variable
De Vylder approximation
Decompounding
dense set of distributions
density functions
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dependent claims
deviation inequalities
Difference equation
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Diffusion-type processes
digital option
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discrete and distributed delays
discrete approximation
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Discrete chaos
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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
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EM-algorithm
empirical means
entire asymptotic separation
Entropic Value-at-Risk
entropy
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entropy power inequality
equilibrium control
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Equivalence in law
ergodic process
ergodic theorem
ergodicity
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 time
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
negative regression dependence
net profit condition
neural networks
non-ergodic process
non-Gaussian limit theorem
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non-Lipschitz coefficients
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nonconcave utility
nonlinear diffusion equation
nonlinear regression
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Nonlinear stochastic differential equation
nonlocal equations
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nonparametric Bayesian estimation
nonparametric estimation
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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
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principal components
probabilistic analysis
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probability metrics
probability of bankruptcy
Process with independent increments
processes with finite variation
progressively equivalent (martingale) measures
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projection problem
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pseudo-gradient
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Q̃-expansion of real numbers
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quadratic variation
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recursive calculation
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regions of stability
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Asymptotic properties of the parabolic equation driven by stochastic measure
Boris Manikin
https://doi.org/10.15559/22-VMSTA213
Pub. online:
6 Sep 2022
Type:
Research Article
Open Access
Journal:
Modern Stochastics: Theory and Applications
Volume 9, Issue 4 (2022), pp. 483–498
Citation
PDF
XML
Abstract
A stochastic parabolic equation on
$[0,T]\times \mathbb{R}$
driven by a general stochastic measure, for which we assume only
σ
-additivity in probability, is considered. The asymptotic behavior of its solution as
$t\to \infty $
is studied.
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AMS -- Americal Mathematical Society
APA -- American Psychological Association 6th ed.
Chicago -- The Chicago Manual of Style 17th ed.
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