24 citations · 92 across the 19 of their papers we have counts for
10 papers · 1 filter
Tamed Feynman-Kac diffusion processes: Killing-branching intertwine
Piotr Garbaczewski, Mariusz Żaba
Relaxation to equilibrium of a drifted Brownian motion is quantified by a transition probability density function, whose main (multiplicative) entry is an inferred Feynman-Kac kern…
Killing versus branching: Unexplored facets of diffusive relaxation
P. Garbaczewski, M. Zaba
We analyze the relaxation dynamics of Feynman-Kac path integral kernel functions in terms of branching diffusion processes with killing. This sheds new light on the admissible path…
(Nonequilibrium) dynamics of diffusion processes with non-conservative drifts
P. Garbaczewski, M. Żaba
The nonequilibrium Fokker-Planck dynamics with a non-conservative drift field, in dimension , can be related with the non-Hermitian quantum mechanics in a real scalar pote…
Levy processes in bounded domains: Path-wise reflection scenarios and signatures of confinement
Piotr Garbaczewski, Mariusz Żaba
We discuss an impact of various (path-wise) reflection-from-the barrier scenarios upon confining properties of a paradigmatic family of symmetric -stable Lévy processes, whose p…
Levy flights in steep potential wells: Langevin modeling versus direct response to energy landscapes
P. Garbaczewski, M. Zaba
We investigate the non-Langevin relative of the Lévy-driven Langevin random system, under an assumption that both systems share a common (asymptotic, stationary, steady-state) targ…
Brownian motion in trapping enclosures: Steep potential wells, bistable wells and false bistability of induced Feynman-Kac (well) potentials
Piotr Garbaczewski, Mariusz Zaba
We investigate signatures of convergence for a sequence of diffusion processes on a line, in conservative force fields stemming from superharmonic potentials , $m=2n…
Path-wise versus kinetic modeling for equilibrating non-Langevin jump-type processes
Mariusz Żaba, Piotr Garbaczewski, Vladimir Stephanovich
We discuss two independent methods of solution of a master equation whose biased jump transition rates account for long jumps of Lévy-stable type and nonetheless admit a Boltzmanni…
Trajectory statistics of confined Lévy flights and Boltzmann-type equilibria
Mariusz Zaba, Piotr Garbaczewski, Vladimir Stephanovich
We analyze a specific class of random systems that are driven by a symmetric Lévy stable noise, where Langevin representation is absent. In view of the Lévy noise sensitivity to en…
Thermalization of Levy flights: Path-wise picture in 2D
Mariusz Zaba, Piotr Garbaczewski
We analyze two-dimensional (2D) random systems driven by a symmetric Lévy stable noise which, under the sole influence of external (force) potentials , asymptotically set do…
Levy flights in confining environments: Random paths and their statistics
M. Zaba, P. Garbaczewski, V. Stephanovich
We analyze a specific class of random systems that are driven by a symmetric Lévy stable noise. In view of the Lévy noise sensitivity to the confining "potential landscape" where j…