Introduction to Stochastic Differential Equations (Second Edition)

Author: Gong Guanglu
Publisher:
Publish Date: 2000-08-01
Features: This book focuses on the strong and weak solutions of stochastic differential equations and their connections with diffusion processes and Markov processes with jumps. Chapter 1 discusses the stochastic integral of Brownian motion. Chapter 2 introduces an outline of the general theory of stochastic processes, emphasizing the duality projection theory of stochastic processes. Chapters 3 and 4 discuss the strong solutions of stochastic differential equations for continuous semimartingales. The weak solutions of It? equations, the existence and uniqueness conditions for the weak solutions of Markovian It? equations, and their connections with diffusion processes. Chapter 5 discusses the one-dimensional case, focusing on the classification of boundary points, recurrence, and conservativeness. Chapter 6 introduces stochastic differential equations with boundaries and diffusion, as well as the Fichera boundary classification. Chapter 7 presents the decomposition of general semimartingales and It?'s formula, the integral of right-continuous, O-limited point processes. It also discusses typical cases with stationary point processes. At the end of the book, there is a brief appendix on the construction of continuous martingales and Brownian motion, as well as the generalized derivative of convex functions.