46 citations · 112 across the 11 of their papers we have counts for
11 papers
Fractional Laplacians and Levy flights in bounded domains
Piotr Garbaczewski
We address Lévy-stable stochastic processes in bounded domains, with a focus on a discrimination between inequivalent proposals for what a boundary data-respecting fractional Lapla…
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…
Probabilistic whereabouts of the "quantum potential"
P. Garbaczewski
We review major appearances of the functional expression in the theory of diffusion-type processes and in quantum mechanically supported dynamical scenarios…
Canonical Quantization and Impenetrable Barriers
P. Garbaczewski, W. Karwowski
We address an apparent conflict between the traditional canonical quantization framework of quantum theory and the spatially restricted quantum dynamics, when the translation invar…
Impenetrable Barriers and Canonical Quantization
P. Garbaczewski, W. Karwowski
We address a conceptual issue of reconciling the traditional canonical quantization framework of quantum theory with the spatially restricted quantum dynamics and the related spect…
Cauchy Noise and Affiliated Stochastic Processes
P. Garbaczewski, R. Olkiewicz
By departing from the previous attempt (Phys. Rev. {\bf E 51}, 4114, (1995)) we give a detailed construction of conditional and perturbed Markov processes, under the assumption tha…
Natural boundaries for the Smoluchowski equation and affiliated diffusion processes
Ph. Blanchard, P. Garbaczewski
The Schrödinger problem of deducing the microscopic dynamics from the input-output statistics data is known to admit a solution in terms of Markov diffusions. The uniqueness of sol…
Schroedinger's Interpolating Dynamics and Burgers' Flows
P. Garbaczewski, G. Kondrat, R. Olkiewicz
We discuss a connection (and a proper place in this framework) of the unforced and deterministically forced Burgers equation for local velocity fields of certain flows, with probab…
Comment on "Why quantum mechanics cannot be formulated as a Markov process"
Piotr Garbaczewski, Robert Olkiewicz
In the paper with the above title, D. T. Gillespie [Phys. Rev. A 49, 1607, (1994)] claims that the theory of Markov stochastic processes cannot provide an adequate mathematical fra…
Nonnegative Feynman-Kac Kernels in Schrödinger's Interpolation Problem
Ph. Blanchard, P. Garbaczewski, R. Olkiewicz
The existing formulations of the Schrödinger interpolating dynamics, which is constrained by the prescribed input-output statistics data, utilize strictly positive Feynman-Kac kern…
The Schroedinger Problem, Levy Processes Noise in Relativistic Quantum Mechanics
P. Garbaczewski, J. R. Klauder, R. Olkiewicz
The main purpose of the paper is an essentially probabilistic analysis of relativistic quantum mechanics. It is based on the assumption that whenever probability distributions aris…