Series on Multivariate Analysis - Vol. 1
MARTINGALES AND STOCHASTIC ANALYSIS
by J Yeh (University of California, Irvine)
This book is a thorough and self-contained treatise of martingales as a tool in stochastic analysis, stochastic integrals and stochastic differential equations. The book is clearly written and details of proofs are worked out.
Contents:
- Stochastic Processes:
- Generated s-Algebras
- Stochastic Processes
- Stopping Times
- Convergence in Lp and Uniform Integrability
- Martingales:
- Martingale, Submartingale and Supermartingale
- Fundamental Submartingale Inequalities
- Convergence of Submartingales
- Uniformly Integrable Submartingales
- Regularity of Sample Functions of Submartingales
- Increasing Processes
- Stochastic Integrals:
- L2-Martingales and Quadratic Variation Processes
- Stochastic Integrals with Respect to Martingales
- Adapted Brownian Motions
- Extensions of the Stochastic Integral
- Itô's Formula
- Itô's Stochastic Calculus
- Stochastic Differential Equations:
- The Space of Continuous Functions
- Definition and Function Space Representation of Solution
- Existence and Uniqueness of Solutions
- Strong Solutions
Readership: Mathematicians.
"This book is a thorough and self-contained treatise of martingales as a tool in stochastic analysis, stochastic integrals and stochastic differential equations. The book is clearly written and details of proofs are worked out."
| Lavoisier-Technique et Documentation |
"... a reader having some knowledge of the theory of stochastic processes and elementary Martingale theory will find it extremely useful because of its clarity, precision, and completeness. It should be of interest to graduate students and researchers in the theory of stochastic processes."
| 516pp |
Pub. date: Dec 1995 |
|
