- ホーム
- > 洋書
- > 英文書
- > Science / Mathematics
Full Description
This book provides an overview of structure-preserving discrete approximations for the probabilistic characteristics of stochastic differential equations, which are essential for understanding stochastic systems in fields such as finance, physics, and engineering. It highlights recent advances in the study of key probabilistic features of discretized systems. In particular, this book presents methods for density approximation and examines the impact of numerical discretizations on hitting probabilities for stochastic ordinary and partial differential equations. The preservation of important asymptotic properties, such as large deviation principles and weak intermittency for parabolic stochastic partial differential equations, is also investigated. A distinctive feature of this book is its demonstration of Malliavin calculus and its adaptation to the analysis of probabilistic properties in discrete settings.
This book is intended for graduate students and researchers with backgrounds in probability theory, stochastic analysis, and numerical analysis who are interested in the analysis and numerical approximation of stochastic differential equations.
Contents
Chapter.1 An Introduction to Malliavin Calculus.- Chapter.2 Density of Langevin Equation and Its Approximation.- Chapter.3 Density of Stochastic Heat Equation and Its Approximation.- Chapter.4 Density of Stochastic Cahn-Hilliard Equation and Its Approximation.- Chapter.5 Hitting Probabilities for Approximations of Systems of Stochastic Heat Equations.- Chapter.6 Asymptotic Preservation of Probabilistic Behaviors of Stochastic Heat Equation.- Gronwall-Type Inequalities.- Itˆo-Taylor Approximation.- Proofs of Propositions 2.4, 4.8, and 6.7 ..- References.- Index.
