10 citations · 22 across the 19 of their papers we have counts for
21 papers
Regularization of the superposition principle: Potential theory meets Fokker-Planck equations
Lucian Beznea, Iulian Cîmpean, Michael Röckner
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 càdlàg Markov processes, which is highly non-trivial and has rema…
Positive solutions to semilinear Dirichlet problems with general boundary data
Lucian Beznea, Alexandra Teodor
We give a probabilistic representation of the solution to a semilinear elliptic Dirichlet problem with general (discontinuous) boundary data. The boundary behaviour of the solution…
Nonlinear Dirichlet forms associated with quasiregular mappings
Camelia Beznea, Lucian Beznea, Michael Roeckner
If is a symmetric, regular, strongly local Dirichlet form on , admitting a carré du champ operator , and is a real number, then one can d…
Strong Feller semigroups and Markov processes: A counter example
Lucian Beznea, Iulian Cîmpean, Michael Röckner
The aim of this note is to show, by providing an elementary way to construct counter-examples, that the strong Feller and the joint (space-time) continuity for a semigroup of Marko…
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…
Path continuity of Markov processes and locality of Kolmogorov operators
Lucian Beznea, Iulian Cîmpean, Michael Röckner
We prove that if we are given a generator of a cadlag Markov process and an open domain in the state space, on which the generator has the local property expressed in a suitabl…
A natural extension of Markov processes and applications to singular SDEs
Lucian Beznea, Iulian Cîmpean, Michael Röckner
We develop a general method for extending Markov processes to a larger state space such that the added points form a polar set. The so obtained extension is an improvement on the s…
Measure-valued branching processes associated with Neumann nonlinear semiflows
Viorel Barbu, Lucian Beznea
We construct a measure-valued branching Markov process associated with a nonlinear boundary value problem, where the boundary condition has a nonlinear pseudo monotone branching me…
Invariant, super and quasi-martingale functions of a Markov process
Iulian Cîmpean, Lucian Beznea
We identify the linear space spanned by the real-valued excessive functions of a Markov process with the set of those functions which are quasimartingales when we compose them with…
From Gaussian estimates for nonlinear evolution equations to the long time behavior of branching processes
L. Beznea, L. I. Ignat, J. D. Rossi
We study solutions to the evolution equation , , in . Here the coefficients verify $ \sum_{k\geqslant 1}q_k…
Quasimartingales associated to Markov processes
Lucian Beznea, Iulian Cîmpean
For a fixed right process we investigate those functions for which is a quasimartingale. We prove that is a quasimartingale if and only if is the dif- fer…
Stochastic equation of fragmentation and branching processes related to avalanches
Lucian Beznea, Madalina Deaconu, Oana Lupascu
We give a stochastic model for the fragmentation phase of a snow avalanche. We construct a fragmentation-branching process related to the avalanches, on the set of all fragmentatio…
A new approach to the existence of invariant measures for Markovian semigroups
Lucian Beznea, Iulian Cîmpean, Michael Röckner
We give a new, two-step approach to prove existence of finite invariant measures for a given Markovian semigroup. First, we identify a convenient auxiliary measure and then we prov…
Measure-valued discrete branching Markov processes
Lucian Beznea, Oana Lupascu
We construct and study branching Markov processes on the space of finite configurations of the state space of a given standard process, controlled by a branching kernel and a killi…
Irreducible recurrence, ergodicity, and extremality of invariant measures for resolvents
Lucian Beznea, Iulian Cîmpean, Michael Röckner
We analyze the transience, recurrence, and irreducibility properties of general sub- Markovian resolvents of kernels and their duals, with respect to a fixed sub-invariant measure…
On the quasi-regularity of non-sectorial Dirichlet forms by processes having the same polar sets
Lucian Beznea, Gerald Trutnau
We obtain a criterion for the quasi-regularity of generalized (non-sectorial) Dirichlet forms, which extends the result of P.J. Fitzsimmons on the quasi-regularity of (sectorial) s…
Potential theory of infinite dimensional Lévy processes
Lucian Beznea, Aurel Cornea, Michael Röckner
We study the potential theory of a large class of infinite dimensional Lévy processes, including Brownian motion on abstract Wiener spaces. The key result is the construction of co…
Quasi-Regular Topologies for L^p-Resolvents and Semi-Dirichlet Forms
Lucian Beznea, Nicu Boboc, Michael Röckner
We prove that for any semi-Dirichlet form on a measurable Lusin space there exists a Lusin topology with the given -algebra as the Borel -algebra so that $(ε,…