Stochastic Differential Equations And Their Numerical Approximations

Stochastic Differential Equations and Their Numerical Approximations

Invariant Measures for Stochastic Nonlinear Schrödinger Equations

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.

Forward-Backward Stochastic Differential Equations and their Applications

This volume is a survey/monograph on the recently developed theory of forward-backward stochastic differential equations (FBSDEs). Basic techniques such as the method of optimal control, the 'Four Step Scheme', and the method of continuation are presented in full. Related topics such as backward stochastic PDEs and many applications of FBSDEs are also discussed in detail. The volume is suitable for readers with basic knowledge of stochastic differential equations, and some exposure to the stochastic control theory and PDEs. It can be used for researchers and/or senior graduate students in the areas of probability, control theory, mathematical finance, and other related fields.