σ-martingale – 135
anomalous diffusion – 97
approximation – 191
averaging principle – 449
backward stochastic differential equation – 415
beta random variable – 97
branching process – 357
change of measures – 43
complete market – 379
compound Poisson process of order k – 395
compound renewal process – 43
conditional processes – 17
confidence ellipsoid – 435
confidence interval – 203
consistent estimator of best prediction – 203
constant dividend strategy – 245
de Vylder approximation – 245
distribution of sumpremum of solution – 79
entropy methods – 79
ergodic process – 339
Euler–Poisson–Darboux equation – 97
exponential functional – 291
extinction – 1
extinction probability – 357
extreme values – 61
filtration – 135
finite mixture model – 435
forward rate – 113
Fourier transform – 97
fractional Brownian motion – 191, 339
game options – 379
Gauss hypergeometric – 357
Gaussian Volterra process – 415
global solution – 1
harmonizable processes – 79
higher-order dispersive equations – 79
Hölder regularity – 449
infinite divisibility – 267
irregular barrier – 157
Itô formula – 415
Kolmogorov-type equation – 291
Lagrange inversion – 357
Lambert-W functions – 357
large deviations – 17
Lévy process – 113
local martingale – 135
Malliavin calculus – 415
market-consistent calibration – 113
martingale – 43, 191
martingale characterization – 395
martingale measures – 43
Mertens decomposition – 157
mild solution – 449
mixture of tempered stable subordinators – 395
mixture with varying concentrations – 435
Monte Carlo method – 245
multi-factor model – 113
multivariate errors-in-variables model – 203
net profit condition – 245
nonlinear diffusion equation – 97
nonlinear regression – 435
nonpersistence in the mean – 1
option pricing – 113
ordinary least squares – 203
Ornstein–Uhlenbeck process – 113
partial differential equation – 415
polynomial errors-in-variables model – 203
post-crisis model – 113
prediction – 203
premium calculation principle – 43
process with independent increments – 291
processes with finite variation – 135
progressively equivalent (martingale) measures – 43
queuing systems – 61
random initial conditions – 79
random velocity – 97
reflected backward doubly stochastic differential equations – 157
regenerative processes – 61
regularly varying distribution – 315
risk model with stochastic premiums – 245
risk process – 221
ruin probability – 221, 245
second Wiener chaos – 267
second-order Galton–Watson process with immigration – 315
semiparametric estimation – 435
short rate – 113
shortfall risk – 379
smoothness of the density – 291
stationary process – 339
stochastic cable equation – 449
stochastic differential equation – 113
stochastic linear growth condition – 157
stochastic Lipschitz condition – 157
stochastic measure – 449
stochastic mutualism model – 1
stochastic optimal control – 379
stochastic partial differential equation – 339
stochastic permanence – 1
stochastic ultimate boundedness – 1
stopping time – 135
strong consistency – 339
strong persistence in the mean – 1
sub-Gaussian processes – 79
sums of Gaussian squares – 267
tail behavior – 315
Volterra type Gaussian processes – 17
Wright – 357
zero-coupon bond – 113