Theory of Martingales

Frontmatter

Part I

Chapter 1. Basic Concepts and the Review of Results of «The General Theory of Stochastic Processes»

R. Sh. Liptser, A. N. Shiryayev

Chapter 2. Semimartingales. I. Stochastic Integral

R. Sh. Liptser, A. N. Shiryayev

Chapter 3. Random Measures and their Compensators

R. Sh. Liptser, A. N. Shiryayev

Chapter 4. Semimartingales. II. Canonical Representation

R. Sh. Liptser, A. N. Shiryayev

Part II

Chapter 5. Weak Convergence of Finite-Dimensional Distributions of Semimartingales to Distributions of Processes with Conditionally Independent Increments

R. Sh. Liptser, A. N. Shiryayev

Chapter 6. The Space D. Relative Compactness of Probability Distributions of Semimartingales

R. Sh. Liptser, A. N. Shiryayev

Chapter 7. Weak Convergence of Distributions of Semimartingales to Distributions of Processes with Conditionally Independent Increments

R. Sh. Liptser, A. N. Shiryayev

Chapter 8. Weak Convergence of Distributions of Semimartingales to the Distribution of a Semimartingale

R. Sh. Liptser, A. N. Shiryayev

Part III

Chapter 9. Invariance Principle and Diffusion Approximation for Models Generated by Stationary Processes

R. Sh. Liptser, A. N. Shiryayev

Chapter 10. Diffusion Approximation for Semimartingales with a Normal Reflection in a Convex Region

R. Sh. Liptser, A. N. Shiryayev

Backmatter