Journal
IMA JOURNAL OF NUMERICAL ANALYSIS
Volume 42, Issue 2, Pages 1789-1805Publisher
OXFORD UNIV PRESS
DOI: 10.1093/imanum/drab023
Keywords
forward-backward stochastic differential equations; linear multistep methods; stability; convergence
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Funding
- Southern University of Science and Technology Start-up Fund [Y01286120]
- National Science Foundation of China [61873325, 11831010]
- China Postdoctoral Science Foundation [2019M651003]
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This paper focuses on the stability analysis of a general class of linear multistep methods for decoupled forward-backward stochastic differential equations (FBSDEs). The general linear multistep methods considered in this study include many well-known linear multistep methods from the ordinary differential equation framework. Under the classical root condition, it is proven that these methods are mean-square stable for decoupled FBSDEs with generator functions related to both y and z. Based on the stability result, a fundamental convergence theorem is further established.
This paper focuses on the stability analysis of a general class of linear multistep methods for decoupled forward-backward stochastic differential equations (FBSDEs). The general linear multistep methods we consider contain many well-known linear multistep methods from the ordinary differential equation framework, such as Adams, Nystrom, Milne--Simpson and backward differentiation formula methods. Under the classical root condition, we prove that general linear multistep methods are mean-square (zero) stable for decoupled FBSDEs with generator function related to both y and z. Based on the stability result, we further establish a fundamental convergence theorem.
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