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Backward stochastic variational inequalities driven by multidimensional fractional Brownian motion

Borkowski D., Jańczak-Borkowska K.

Opuscula Mathematica

2018

Vol. 38, no. 3

307--326

We study the existence and uniqueness of the backward stochastic variational inequalities driven by m-dimensional fractional Brownian motion with Hurst parameters Hk (k = 1,... m) greater than 1/2. The stochastic integral used throughout the paper is the divergence type integral.

Generalized RBSDEs with random terminal time and applications to PDEs

Jańczak-Borkowska K.

Bulletin of the Polish Academy of Sciences. Mathematics

2011

Vol. 59, no 1

85-100

Generalized reflected backward stochastic differential equations have been considered so far only in the case of a deterministic interval. In this paper the existence and uniqueness of solution for generalized reflected backward stochastic differential equations in a convex domain with random terminal time is studied. Applications to the obstacle problem with Neumann boundary conditions for partial differential equations of elliptic type are given.