ON A WASSERSTEIN-TYPE DISTANCE BETWEEN SOLUTIONS TO STOCHASTIC DIFFERENTIAL EQUATIONS
成果类型：
Article
署名作者：
Bion-Nadal, Jocelyne; Talay, Denis
署名单位：
Institut Polytechnique de Paris; Ecole Polytechnique; Inria; Universite Cote d'Azur
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/18-AAP1423
发表日期：
2019
页码：
1609-1639
关键词：
摘要：
In this paper, we introduce a Wasserstein-type distance on the set of the probability distributions of strong solutions to stochastic differential equations. This new distance is defined by restricting the set of possible coupling measures. We prove that it may also be defined by means of the value function of a stochastic control problem whose Hamilton-Jacobi-Bellman equation has a smooth solution, which allows one to deduce a priori estimates or to obtain numerical evaluations. We exhibit an optimal coupling measure and characterize it as a weak solution to an explicit stochastic differential equation, and we finally describe procedures to approximate this optimal coupling measure. A notable application concerns the following modeling issue: given an exact diffusion model, how to select a simplified diffusion model within a class of admissible models under the constraint that the probability distribution of the exact model is preserved as much as possible?