Weak convergence of path-dependent SDEs with irregular coefficients

2018/09/10 by Jianhai Bao, Jinghai Shao, Bao, Jianhai +1 · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1809.03088

openalex publication_date 2018/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we develop via Girsanov's transformation a perturbation argument to investigate weak convergence of Euler-Maruyama (EM) scheme for path-dependent SDEs with Hölder continuous drifts. This approach is available to other scenarios, e.g., truncated EM schemes for non-degenerate SDEs with finite memory or infinite memory. Also, such trick can be applied to study weak convergence of truncated EM scheme for a range of stochastic Hamiltonian systems with irregular coefficients and with memory, which are typical degenerate dynamical systems. Moreover, the weak convergence of path-dependent SDEs under integrability condition is investigated by establishing, via the dimension-free Harnack inequality, exponential integrability of irregular drifts w.r.t. the invariant probability measure constructed explicitly in advance.

Citations

• Hypercontractivity for Stochastic Hamiltonian Systems

Cited by

• Weak convergence of path-dependent SDEs driven by fractional Brownian motion with irregular coefficients

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