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, Itô integration, stochastic analysis, stochastic differential equations, fractional Brownian motion and parameter estimation in diffusion models.
Table of Content
Part1.Theory of Stochastic Processes.
1. Stochastic Processes. General Properties. Trajectories, Finite-dimensional Distributions.
2. Stochastic Processes with Independent Increments.
3. Gaussian Processes. Integration with Respect to Gaussian Processes.
4. Construction, Properties and Some Functionals of the Wiener Process and Fractional Brownian Motion.
5. Martingales and Related Processes.
6. Regularity of Trajectories of Stochastic Processes.
7. Markov and Diffusion Processes.
8. Stochastic Integration.
9. Stochastic Differential Equations.
Part 2. Statistics of Stochastic Processes.
10. Parameter Estimation.
11. Filtering Problem. Kalman-Bucy Filter.
About the author
Yuliya Mishura, National University of Kyiv, Ukraine Georgiy Shevchenko, National University of Kyiv, Ukraine
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