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Related papers: Tempered Fractional Feynman-Kac Equation

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We study the one-dimensional motion of a Brownian particle inside a confinement described by two reactive boundaries which can partially reflect or absorb the particle. Understanding the effects of such boundaries is important in physics,…

Statistical Mechanics · Physics 2021-03-30 Arnab Pal , Isaac Pérez Castillo , Anupam Kundu

We introduce a fractional Fokker-Planck equation with a temporal power-law dependence on the drift force fields. For this case, the moments of the tracer from the force-force correlation in terms of the time-dependent drift force fields are…

Statistical Mechanics · Physics 2007-05-23 Kyungsik Kim , Y. S. Kong

In this Letter, we clarify the physical origin of effective transport in periodic and tilted periodic systems. When Brownian dynamics is examined on the scale of a single period, the particle displacement admits a natural separation into a…

Statistical Mechanics · Physics 2026-01-27 Sang Yang , Zhixin Peng

This paper studies the intermediate time behaviour of a small random perturbation of a periodic cellular flow. Our main result shows that on time scales shorter than the diffusive time scale, the limiting behaviour of trajectories that…

Probability · Mathematics 2016-09-09 Martin Hairer , Gautam Iyer , Leonid Koralov , Alexei Novikov , Zsolt Pajor-Gyulai

The present paper investigates the effects of tempering the power law kernel of moving average representation of a fractional Brownian motion (fBm) on some local and global properties of this Gaussian stochastic process. Tempered fractional…

Probability · Mathematics 2020-05-27 Ehsan Azmoodeh , Yuliya Mishura , Farzad Sabzikar

Fractional tempered stable motion (fTSm)} is defined and studied. FTSm has the same covariance structure as fractional Brownian motion, while having tails heavier than Gaussian but lighter than stable. Moreover, in short time it is close to…

Probability · Mathematics 2023-04-11 C. Houdré , R. Kawai

Levy flights and fractional Brownian motion (fBm) have become exemplars of the heavy tailed jumps and long-ranged memory widely seen in physics. Natural time series frequently combine both effects, and linear fractional stable motion (lfsm)…

Mathematical Physics · Physics 2011-08-25 N. W. Watkins , D. Credgington , R. Sanchez , S. J. Rosenberg , S. C. Chapman

We derive, through subordination techniques, a generalized Feynman-Kac equation in the form of a time fractional Schrodinger equation. We relate such equation to a functional which we name the subordinated local time. We demonstrate through…

Statistical Mechanics · Physics 2023-05-01 Toby Kay , Luca Giuggioli

The unified description of diffusion processes that cross over from a ballistic behavior at short times to normal or anomalous diffusion (sub- or superdiffusion) at longer times is constructed on the basis of a non-Markovian generalization…

Statistical Mechanics · Physics 2013-03-26 Valery Ilyin , Itamar Procaccia , Anatoly Zagorodny

We consider time-changed Brownian motions on random Koch (pre-fractal and fractal) domains where the time change is given by the inverse to a subordinator. In particular, we study the fractional Cauchy problem with Robin condition on the…

Probability · Mathematics 2020-12-23 Raffaela Capitanelli , Mirko D'Ovidio

Anomalous dynamics characterized by non-Gaussian probability distributions (PDFs) and/or temporal long-range correlations can cause subtle modifications of conventional fluctuation relations. As prototypes we study three variants of a…

Statistical Mechanics · Physics 2015-07-16 P. Dieterich , R. Klages , A. V. Chechkin

We study the distribution of first passage time (FPT) in Levy type of anomalous diffusion. Using recently formulated fractional Fokker-Planck equation we obtain three results. (1) We derive an explicit expression for the FPT distribution in…

Statistical Mechanics · Physics 2009-11-07 Govindan Rangarajan , Mingzhou Ding

This paper reviews the formulation of the Feynman-Vernon model of linear dissipative systems for a standard Brownian particle moving in an external potential $V(x,t)$ and introduces the formulation of a generalized oscillator model of a…

Quantum Physics · Physics 2018-03-29 Marco Patriarca

An intermittent nonlinear map generating subdiffusion is investigated. Computer simulations show that the generalized diffusion coefficient of this map has a fractal, discontinuous dependence on control parameters. An amended continuous…

We consider different types of processes obtained by composing Brownian motion $B(t)$, fractional Brownian motion $B_{H}(t)$ and Cauchy processes $% C(t)$ in different manners. We study also multidimensional iterated processes in…

Probability · Mathematics 2010-08-06 Luisa Beghin , Enzo Orsingher , Lyudmyla Sakhno

Meerschaert and Sabzikar [12], [13] introduced tempered fractional Brownian/stable motion (TFBM/TFSM) by including an exponential tempering factor in the moving average representation of FBM/FSM. The present paper discusses another tempered…

Probability · Mathematics 2017-02-24 Farzad Sabzikar , Donatas Surgailis

We present a spectral-theoretic approach to time-average statistical mechanics for general, non-equilibrium initial conditions. We consider the statistics of bounded, local additive functionals of reversible as well as irreversible ergodic…

Statistical Mechanics · Physics 2020-10-21 Alessio Lapolla , David Hartich , Aljaž Godec

Mass transport problems are ubiquitous in diverse fields of physics and engineering. With the development of fractional calculus, many have taken to studying problems of fractional mass transport either through numerical simulations or…

Mathematical Physics · Physics 2025-06-18 Nathaniel G. Hermann , M. Shane Hutson

We introduce fractional Brownian motion processes (fBm) as an alternative model for the turbulent index of refraction. These processes allow to reconstruct most of the index properties, but they are not differentiable. We overcome the…

Optics · Physics 2007-05-23 Dario G Perez

Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces.…

Statistical Mechanics · Physics 2023-05-10 Johan du Buisson , Hugo Touchette