Reflected BSDEs and continuous solutions of parabolic obstacle problem for semilinear PDEs in divergence form

Tomasz Klimsiak

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arXiv · 0912.2193

Reflected BSDEs and continuous solutions of parabolic 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 eqution and mild conditions on the obstacle a unique continuous solution of the problem admits a stochastic representation in terms of reflected backward stochastic differential equations. We derive also some regularity properties of so- lutions and prove useful approximation results.

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Tomasz Klimsiak. 2009-12-11. Reflected BSDEs and continuous solutions of parabolic obstacle problem for semilinear PDEs in divergence form. https://arxiv.org/abs/0912.2193

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