Diffusion processes with weak constraint through penalization approximation

2017/04/05 by Jean-François Jabir, Jabir, Jean-Francois
Economics, Econometrics and Finance · Mathematics · #35E10 #39A50 #60J60 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1704.01505

openalex publication_date 2017/04/05 · openalex created_date 2017/04/28 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the construction of a diffusion process whose time-marginal densities are constrained to belong to a given set at all time. The construction is obtained from a penalization approximation to the constraint set, acting on the Wasserstein distance W2 to the constraint space. Under some technical assumptions on the constraint space and the initial distribution of the model, the penalization approximation yields to a stochastic differential equation analogous to the Skorohod problem of reflected diffusion.

Citations

• Statistics of Random Processes

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