Sticky Brownian motions and a probabilistic solution to a two-point boundary value problem

2018/10/15 by Thu Dang Thien Nguyen, Nguyen, Thu Dang Thien
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #advanced mathematical theories #math.PR

paper · pdf · doi:10.48550/arxiv.1810.06199

arxiv created 2018/10/15 · openalex publication_date 2018/10/15 · arxiv updated 2018/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study a two-point boundary value problem consisting of the heat equation on the open interval (0,1) with boundary conditions which relate first and second spatial derivatives at the boundary points. Moreover, the unique solution to this problem can be represented probabilistically in terms of a sticky Brownian motion. This probabilistic representation is attained from the stochastic differential equation for a sticky Brownian motion on the bounded interval [0,1].

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