Necessary and sufficient conditions for global-in-time existence of solutions of ordinary, stochastic, and parabolic differential equations.
Nonlinear evolution equations on Banach space.
Nonlinear stochastic heat equations with cubic nonlinearities and additive -regular noise in .
Note on some variational problem related to statistical solutions of differential equations in Banach spaces
The properties of statistical solutions for some general differential equations in Banach spaces are investigated.
Numerical schemes for multivalued backward stochastic differential systems
We define approximation schemes for generalized backward stochastic differential systems, considered in the Markovian framework. More precisely, we propose a mixed approximation scheme for the following backward stochastic variational inequality: where ∂φ is the subdifferential operator of a convex lower semicontinuous function φ and (X t)t∈[0;T] is the unique solution of a forward stochastic differential equation. We use an Euler type scheme for the system of decoupled forward-backward variational...