Cauchy Noise and Affiliated Stochastic Processes

Abstract

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 that the Cauchy law of probability replaces the Gaussian law (appropriate for the Wiener process) as the model of primordial noise. All considered processes are regarded as probabilistic solutions of the so-called Schrödinger interpolation problem, whose validity is thus extended to the jump-type processes and their step process approximants.

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References in corpus (1)

• Burgers velocity fields and dynamical transport processes

Cited by in corpus (12)

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• Heat and work distributions for mixed Gauss-Cauchy process
• Nonlocally-induced (fractional) bound states: Shape analysis in the infinite Cauchy well
• Lévy-Schrödinger wave packets
• Markov processes and generalized Schroedinger equations
• Levy flights in confining environments: Random paths and their statistics
• Thermalization of Levy flights: Path-wise picture in 2D