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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Acknowledgements
I would like to express my sincere gratitude to Prof. Errico Presutti for his great ideas which help me a lot to complete this paper.
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Nguyen, T.D.T. Sticky Brownian Motions and a Probabilistic Solution to a Two-Point Boundary Value Problem. Math Phys Anal Geom 24, 10 (2021). https://doi.org/10.1007/s11040-021-09383-5
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DOI: https://doi.org/10.1007/s11040-021-09383-5