Approximations to Probabilistic Characteristics of Stochastic Differential Equations / by Jianbo Cui, Jialin Hong, Derui Sheng.

Format:

Book

Author/Creator:

Cui, Jianbo., Author.

Hong, Jialin., Author.

Sheng, Derui., Author.

Series:

Lecture Notes in Mathematics, 1617-9692 ; 2391

Language:

English

Subjects (All):

Numerical analysis.

Probabilities.

Stochastic analysis.

Stochastic processes.

Differential equations.

Numerical Analysis.

Probability Theory.

Stochastic Analysis.

Stochastic Processes.

Differential Equations.

Local Subjects:

Numerical Analysis.

Probability Theory.

Stochastic Analysis.

Stochastic Processes.

Differential Equations.

Physical Description:

1 online resource (XIV, 380 p. 1 illus.).

Edition:

1st ed. 2026.

Place of Publication:

Singapore : Springer Nature Singapore : Imprint: Springer, 2026.

Summary:

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.

Notes:

Print version record.

ISBN:

9789819588138

OCLC:

1614875827