Weak convergence of path-dependent SDEs with irregular coefficients

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.

arXiv comment24 pages

References in corpus (4)

• Harnack Inequalities for Functional SDEs with Multiplicative Noise and Applications
• Harnack inequality for SDE with multiplicative noise and extension to Neumann semigroup on nonconvex manifolds
• A duality approach for the weak approximation of stochastic differential equations
• Hypercontractivity for Stochastic Hamiltonian Systems

Cited by in corpus (5)

• On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift
• Probability density function of SDEs with unbounded and path--dependent drift coefficient
• Weak convergence of path-dependent SDEs driven by fractional Brownian motion with irregular coefficients
• Weak convergence of Euler scheme for SDEs with singular drift
• Central limit theorem and Self-normalized Cramér-type moderate deviation for Euler-Maruyama Scheme