Jialin Hong - Böcker
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5 produkter
5 produkter
Del 2314 - Lecture Notes in Mathematics
Symplectic Integration of Stochastic Hamiltonian Systems
Häftad, Engelska, 2023
464 kr
Skickas inom 5-8 vardagar
This book provides an accessible overview concerning the stochastic numerical methods inheriting long-time dynamical behaviours of finite and infinite-dimensional stochastic Hamiltonian systems. The long-time dynamical behaviours under study involve symplectic structure, invariants, ergodicity and invariant measure. The emphasis is placed on the systematic construction and the probabilistic superiority of stochastic symplectic methods, which preserve the geometric structure of the stochastic flow of stochastic Hamiltonian systems.The problems considered in this book are related to several fascinating research hotspots: numerical analysis, stochastic analysis, ergodic theory, stochastic ordinary and partial differential equations, and rough path theory. This book will appeal to researchers who are interested in these topics.
634 kr
Skickas inom 5-8 vardagar
Del 2251 - Lecture Notes in Mathematics
Invariant Measures for Stochastic Nonlinear Schrödinger Equations
Numerical Approximations and Symplectic Structures
Häftad, Engelska, 2019
325 kr
Skickas inom 5-8 vardagar
This book provides some recent advance in the study of stochastic nonlinear Schrödinger equations and their numerical approximations, including the well-posedness, ergodicity, symplecticity and multi-symplecticity. It gives an accessible overview of the existence and uniqueness of invariant measures for stochastic differential equations, introduces geometric structures including symplecticity and (conformal) multi-symplecticity for nonlinear Schrödinger equations and their numerical approximations, and studies the properties and convergence errors of numerical methods for stochastic nonlinear Schrödinger equations.This book will appeal to researchers who are interested in numerical analysis, stochastic analysis, ergodic theory, partial differential equation theory, etc.
Approximations to Probabilistic Characteristics of Stochastic Differential Equations
Häftad, Engelska, 2026
1 265 kr
Kommande
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.
Del 2341 - Lecture Notes in Mathematics
Numerical Approximations of Stochastic Maxwell Equations
via Structure-Preserving Algorithms
Häftad, Engelska, 2024
640 kr
Skickas inom 10-15 vardagar
The stochastic Maxwell equations play an essential role in many fields, including fluctuational electrodynamics, statistical radiophysics, integrated circuits, and stochastic inverse problems.