Reflected BSDEs and obstacle problem for semilinear PDEs in divergence form

Tomasz Klimsiak

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arXiv · 1810.03392

Reflected BSDEs and obstacle problem for semilinear PDEs in divergence form

Tomasz Klimsiak

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Abstract

We consider the Cauchy problem for semilinear parabolic equation in divergence form with obstacle. We show that under natural conditions on the right-hand side of the equation and mild conditions on the obstacle the problem has a unique solution and we provide its stochastic representation in terms of reflected backward stochastic differential equations. We prove also regularity properties and approximation results for solutions of the problem.

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Tomasz Klimsiak. 2018-10-08. Reflected BSDEs and obstacle problem for semilinear PDEs in divergence form. https://arxiv.org/abs/1810.03392

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