Langevin equation with a multiplicative stochastic force is considered. That force is uncorrelated, it has the Lévy distribution and the power-law intensity. The Fokker-Planck equations, which correspond both to the Itô and Stratonovich interpretation, are presented. They are solved for the case without drift and for the harmonic oscillator potential. The variance is evaluated; it is always infinite for the Itô case whereas for the Stratonovich one it can be finite and rise with time slower that linearly, which indicates subdiffusion. Analytical results are compared with numerical simulations.
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http://dx.doi.org/10.1103/PhysRevE.80.051113 | DOI Listing |
Phys Rev E
April 2023
University of Lille, Unité de Glycobiologie Structurale et Fonctionnelle (UGSF), CNRS UMR8576, F-59000 Lille, France.
Geometric Brownian motion is an exemplary stochastic processes obeying multiplicative noise, with widespread applications in several fields, e.g., in finance, in physics, and biology.
View Article and Find Full Text PDFPhys Rev E
October 2022
Department of Physics, PUC-Rio, Rua Marquês de São Vicente 225, 22451-900 Rio de Janeiro, Brazil.
We address the problem of random search for a target in an environment with a space-dependent diffusion coefficient D(x). Considering a general form of the diffusion differential operator that includes Itô, Stratonovich, and Hänggi-Klimontovich interpretations of the associated stochastic process, we obtain and analyze the first-passage-time distribution and use it to compute the search efficiency E=〈1/t〉. For the paradigmatic power-law diffusion coefficient D(x)=D_{0}|x|^{α}, where x is the distance from the target and α<2, we show the impact of the different interpretations.
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June 2022
Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada.
Lattice Monte Carlo (LMC) simulations are widely used to investigate diffusion-controlled problems such as drug-release systems. The presence of an inhomogeneous diffusivity environment raises subtle questions about the interpretation of stochastic dynamics in the overdamped limit, an issue sometimes referred to as the "Ito-Stratonovich-isothermal dilemma." We propose a LMC formalism that includes the different stochastic interpretations in order to model the diffusion of particles in a space-dependent diffusivity landscape.
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May 2021
Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France.
We present an alternative form of intermittency, Lévy on-off intermittency, which arises from multiplicative α-stable white noise close to an instability threshold. We study this problem in the linear and nonlinear regimes, both theoretically and numerically, for the case of a pitchfork bifurcation with fluctuating growth rate. We compute the stationary distribution analytically and numerically from the associated fractional Fokker-Planck equation in the Stratonovich interpretation.
View Article and Find Full Text PDFPhys Rev E
October 2020
Department of Physics, PUC-Rio, Rua Marquês de São Vicente 225, 22451-900, Rio de Janeiro, RJ, Brazil.
Population survival depends on a large set of factors and on how they are distributed in space. Due to landscape heterogeneity, species can occupy particular regions that provide the ideal scenario for development, working as a refuge from harmful environmental conditions. Survival occurs if population growth overcomes the losses caused by adventurous individuals that cross the patch edge.
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