Description
In this book, the authors present the modern approaches to study stochastic processes and modern tools for their statistical analysis. It covers the following topics for stochastic processes: general properties of stochastic processes, trajectories and their regularity, finite-dimensional distributions, processes with independent increments, Gaussian processes, Wiener process, Levy processes, fractional, multifractional and fractal processes, Markov chains and processes, diffusion processes, functional limit theorems for stochastic processes, stochastic integration, stochastic differential equations, stationery processes, processes with short and long range dependence. Statistical estimation methods will be presented both in nonparametric and parametric settings, in time and spectral domain. Each chapter will be supplied with a certain number of exercises providing a better understanding of the subject.
