Work

On time uniform Wong-Zakai approximation theorems

Year: 2025

Type: article

Abstract: We consider the long time behavior of Wong-Zakai approximations of stochastic differential equations. These piecewise smooth diffusion approximations are of great importance in many areas, such as those with ordinary differential equations associated to random smooth fluctuations; e.g. robust filtering problems. In many examples, the mean error estimate bounds that have been derived in the literature can grow exponentially with respect to the time horizon. We show in a simple example that indeed mean error estimates do explode exponentially in the time parameter, i.e. in that case a Wong-Zakai approximation is only useful for extremely short time intervals. Under spectral conditions, we present some quantitative time-uniform convergence theorems, i.e. time-uniform mean error bounds, yielding what seems to be the first results of this type for Wong-Zakai diffusion approximations.

Source: Mathematics of Computation

DOI: 10.1090/mcom/4112

Authors: Pierre Del Moral, Shulan Hu, Ajay Jasra, Hamza Ruzayqat, Xinyu Wang

Institutions: Institut de Mathématiques de Bordeaux, Zhongnan University of Economics and Law, Chinese University of Hong Kong, Chinese University of Hong Kong, Shenzhen, King Abdullah University of Science and Technology

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

Funders: Zhongnan University of Economics and Law, King Abdullah University of Science and Technology, Fundamental Research Funds for the Central Universities, Trường Đại học Kinh tế - Luật, Đại học Quốc gia Thành phố Hồ Chí Minh

Awards: G4070883207, G876340298