Cauchy Problem for Semilinear Parabolic Equation with Time-Dependent Obstacles: A BSDEs Approach
Cauchy Problem for Semilinear Parabolic Equation with Time-Dependent Obstacles: A BSDEs Approach
In the paper we apply methods of the theory of backward stochastic differential equations to prove existence, uniqueness and stochastic representation of solutions of the Cauchy problem for semilinear parabolic equation in divergence form with two time-dependent obstacles. We consider two quite different cases: problems with distinct quasi-continuous obstacles and …