AIC and BIC criteria – 51
approximation rate – 401
asymptotic consistency – 147
asymptotic normality – 17, 343
autoregressive models – 51, 67
Berkson model – 131
binary regression – 131
Brownian motion – 185
central limit theorem – 29
cointegration – 51, 67
compact operator – 147
consistency – 343
continuous additive functional – 107
convergence – 203
decompounding – 1
discrete chaos – 327
discrete-time approximations – 355
discretized model – 17
drift parameter – 17
econometrics time series – 51, 67
equivalence in law – 287
errors in variables – 131
Euler–Maruyama scheme – 355
exponential bound – 173
faithfulness of fine packing system for packing dimension calculation – 371
Feynman–Kac semigroup – 107
Feynman–Kac formula – 251
financial markets – 233, 355
finite mixture model – 343
finite-time ruin probability – 421
Fourier transform – 327
fractional Brownian motion – 29, 147, 219
fractional integral – 219
Gärtner–Ellis condition – 267
Gaussian distribution – 95
Gaussian process – 267
Gaussian sheets – 287
generalized log-Pareto distribution – 391
Granger causality – 51, 67
Hausdorff–Besicovitch dimension of a set – 371
Hellinger distance – 391
increasing path – 185
inhomogeneous model – 173, 421
integral equation with weakly singular kernel – 147
integral functional – 165, 251, 401
integral representation – 219
jump-diffusion process – 203
Kato class – 107
Laplace transform – 267
limit theorem – 327
linear regression – 297, 343
logistic regression – 131
Lundberg-type inequality – 173
Malliavin calculus – 29
Markov processes – 165, 251, 401
maximal residual – 297
maximum likelihood estimator – 147
minimax estimator – 297
mixture with varying concentrations – 343
multidimensional compound Poisson process – 1
multiparameter Gaussian processes – 287
multiple Wiener integrals – 29
nonparametric Bayesian estimation – 1
nonparametric estimation – 343
occupation-time option – 251
option pricing – 233, 355
Ornstein–Uhlenbeck process – 233, 355
packing dimension of a set – 371
packing-dimension-preserving transformations – 371
Poisson measure – 203
posterior contraction rate – 1
quadratic variation – 29
randomized periodogram – 29
rate of convergence – 95, 165
regression calibration model – 131
renewal model – 173
representation of Gaussian processes – 287
ruin probability – 173
series expansions – 287
set indexed process – 185
simulation – 309
small deviation – 219
stochastic differential equation – 17, 203
stochastic nonstationarity – 51, 67
stochastic volatility – 233, 355
stopping time – 203
strong approximation – 165
sub-Gaussian random processes – 309
three-seasonal model – 421
transition probability density – 107
trends and breaks – 51, 67
truncated pseudomoments – 95
ultimate ruin probability – 421
variational distance – 391
von-Mises type parameterization – 391
weak approximation rates – 251
Wiener–Itô integral – 327