This book is concerned with the theory of stochastic processes and the theoretical aspects of statistics for stochastic processes. It combines classic topics such as construction of stochastic processes, associated filtrations, processes with independent increments, Gaussian processes, martingales, Markov properties, continuity and related properties of trajectories with contemporary subjects: integration with respect to Gaussian processes, Itȏ integration, stochastic analysis, stochastic differential equations, fractional Brownian motion and parameter estimation in diffusion models.

Yuliya Mishura is Full Professor and Head of the Department of Probability Theory, Statistics and Actuarial Mathematics at Taras Shevchenko National University of Kyiv. Her research interests include martingale theory, fractional processes, stochastic differential equations, the statistics of stochastic processes and financial mathematics.

Georgiy Shevchenko is Full Professor in the Department of Probability Theory, Statistics and Actuarial Mathematics at Taras Shevchenko National University of Kyiv. His research interests include stochastic analysis, stochastic differential equations, models with long memory, the statistics of stochastic processes and financial mathematics.