Conservative methods for stochastic differential equations with a conserved quantity

2014/11/06 by Chuchu Chen, David Cohen, Chen, Chuchu +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · #Differential Equations and Numerical Methods #FOS: Mathematics #Financial Risk and Volatility Modeling #Numerical Analysis (math.NA) #Statistical Methods and Inference #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1411.1819

openalex publication_date 2014/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper proposes a novel conservative method for numerical computation of general stochastic differential equations in the Stratonovich sense with a conserved quantity. We show that the mean-square order of the method is 1 if noises are commutative and that the weak order is also 1. Since the proposed method may need the computation of a deterministic integral, we analyse the effect of the use of quadrature formulas on the convergence orders. Furthermore, based on the splitting technique of stochastic vector fields, we construct conservative composition methods with similar orders as the above method. Finally, numerical experiments are presented to support our theoretical results.

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