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

Thu Dang Thien Nguyen

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arXiv · 1810.06199

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

Thu Dang Thien Nguyen

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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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Thu Dang Thien Nguyen. 2018-10-15. Sticky Brownian motions and a probabilistic solution to a two-point boundary value problem. https://arxiv.org/abs/1810.06199

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