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

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

2009-12-11

arxiv.org/abs/0912.2193v1

Mathematics

Probability

36 pages, 33rd Conference on Stochastic Processes and Their Applications, Berlin 2009

Scientific paper

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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