Mishura Y., Shevchenko G. Theory and Statistical Applications of Stochastic Processes

ISTE Ltd and John Wiley & Sons, Inc., 2017. — 400 p. — (Mathematics and Statistics). — ISBN13: 9781119476634.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, It? integration, stochastic analysis, stochastic differential equations, fractional Brownian motion and parameter estimation in diffusion models.Theory of Stochastic Processes
Stochastic Processes. General Properties. Trajectories, Finite-dimensional Distributions
Stochastic Processes with Independent Increments
Gaussian Processes. Integration with Respect to Gaussian Processes
Construction, Properties and Some Functionals of the Wiener Process and Fractional Brownian Motion
Martingales and Related Processes
Regularity of Trajectories of Stochastic Processes
Markov and Diffusion Processes
Stochastic Integration
Stochastic Differential Equations
Statistics of Stochastic Processes
Parameter Estimation
Filtering Problem. Kalman-Bucy Filter