On classical solutions of boundary value problems for certain nonlinear integro-differential equations (Q1901209)

The authors consider nonlinear convex parabolic integro-differential equations of second order. The solvability of the Dirichlet and Neumann boundary value problems in the class of functions \(C^{2+\alpha}\) are proved using methods of the theory of stochastic processes. Applications to the Bellman equation arising in the theory of controlled stochastic processes are given.