5 papers
Regularization of the superposition principle: Potential theory meets Fokker-Planck equations
Lucian Beznea, Iulian Cîmpean, Iulian Cîmpean +2
For a solution to a (possibly nonlinear) Fokker-Planck equation (FPE) the powerful superposition principle renders a probability measure on path space with one dimensional time mar…
Continuous flows driving Markov processes and multiplicative -semigroups
Lucian Beznea, Mounir Bezzarga, Iulian Cimpean
We develop a method of driving a Markov processes through a continuous flow. In particular, at the level of the transition functions we investigate an approach of adding a first or…
Nonlinear Dirichlet problem of non-local branching processes
Lucian Beznea, Oana Lupascu-Stamate, Alexandra Teodor
We present a method of solving a nonlinear Dirichlet problem with discontinuous boundary data and we give a probabilistic representation of the solution using the nonlocal branchin…
Construction of Hunt processes by the Lyapunov method and applications to generalized Mehler semigroups
Lucian Beznea, Iulian Cîmpean, Michael Röckner
In this paper we deal with the problem of characterizing those generalized Mehler semigroups that do correspond to cà dlà g Markov processes, which is highly non-trivial and has re…
From Monte Carlo to neural networks approximations of boundary value problems
Lucian Beznea, Iulian Cimpean, Oana Lupascu-Stamate +2
In this paper we study probabilistic and neural network approximations for solutions to Poisson equation subject to Holder data in general bounded domains of . We aim…