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Motivated by empirical data, we develop a statistical description of the queue dynamics for large tick assets based on a two-dimensional Fokker-Planck (diffusion) equation, that explicitly includes state dependence, i.e. the fact that the…

Trading and Market Microstructure · Quantitative Finance 2013-09-25 A. Gareche , G. Disdier , J. Kockelkoren , J. -P. Bouchaud

The equilibrium distribution function determines macroscopic observables in statistical physics. While conventional methods correct equilibrium distributions in weakly nonlinear or near-integrable systems, they fail in strongly nonlinear…

Statistical Mechanics · Physics 2025-07-11 Jialin Zhang , Yong Zhang , Hong Zhao

The concern of the present paper is the design of efficient numerical schemes for a specific Fokker-Planck equation describing the dynamics of energetic particles occurring in thermonuclear fusion plasmas (runaway electrons for example). In…

Analysis of PDEs · Mathematics 2025-09-08 Hugo Parada , Claudia Negulescu

Adopting a bottom-up perspective, we propose a novel two-parametric nonadditive entropy, $S_{\kappa\ell}$, associated with a Kappa-type power-law velocity distribution, $F_{\kappa\ell}(v)$, recently derived in the literature. By formulating…

Statistical Mechanics · Physics 2025-12-04 J. A. S. Lima , M. H. Benetti

We study Markov processes associated with stochastic differential equations, whose non-linearities are gradients of convex functionals. We prove a general result of existence of such Markov processes and a priori estimates on the transition…

Probability · Mathematics 2007-05-23 Luigi Ambrosio , Giuseppe Savare , Lorenzo Zambotti

The fractional Fokker-Planck equation for subdiffusion in time-dependent force fields is derived from the underlying continuous time random walk. Its limitations are discussed and it is then applied to the study of subdiffusion under the…

Statistical Mechanics · Physics 2009-06-02 E. Heinsalu , M. Patriarca , I. Goychuk , P. Hanggi

We study the diffusion of charged particles in the weakly ionized plasma with the power-law kappa-distributions and without magnetic field. The electrons and ions have different kappa-parameters. We obtain the expressions of both diffusion…

Plasma Physics · Physics 2020-02-04 Lan Wang , Jiulin Du

Inspired by the modeling of grain growth in polycrystalline materials, we consider a nonlinear Fokker-Plank model, with inhomogeneous diffusion and with variable mobility parameters. We develop large time asymptotic analysis of such…

Analysis of PDEs · Mathematics 2022-06-24 Yekaterina Epshteyn , Chang Liu , Chun Liu , Masashi Mizuno

A mapping of nonextensive statistical mechanics into Gibbs' statistical mechanics exists, which leads to a generalization of Einstein's formula for fluctuations. A unified treatment of stability of relaxed states in nonextensive statistical…

Classical Physics · Physics 2018-01-30 Andrea Di Vita

This work is devoted to the formulation and derivation of the $\kappa-\mu$/gamma distribution which corresponds to A physical fading model. This distribution is composite and is based on the well known $\kappa-\mu$ generalized multipath…

Information Theory · Computer Science 2015-05-19 Paschalis C. Sofotasios , Steven Freear

Stochastic dynamics in the energy representation is employed as a method to study non-equilibrium Brownian-like systems. It is shown that the equation of motion for the energy of such systems can be taken in the form of the Langevin…

Statistical Mechanics · Physics 2015-05-18 Bohdan I. Lev , Alexei D. Kiselev

This paper is concerned with the Fokker-Planck (FP) description of classical stochastic systems with discrete time delay. The non-Markovian character of the corresponding Langevin dynamics naturally leads to a coupled infinite hierarchy of…

Statistical Mechanics · Physics 2018-07-03 Sarah A. M. Loos , Sabine H. L. Klapp

In this article, we retain the basic idea and at the same time generalize Kawasaki's dynamics, spin-pair exchange mechanism, to spin-pair redistribution mechanism, and present a normalized redistribution probability. This serves to unite…

Disordered Systems and Neural Networks · Physics 2009-11-07 Han Zhu , Jian-Yang Zhu

We suggest that coarsening dynamics can be described in terms of a generalized random walk, with the dynamics of the growing length $L(t)$ controlled by a drift term, $\mu(L)$, and a diffusive one, ${\cal D}(L)$. We apply this…

Statistical Mechanics · Physics 2018-09-19 Federico Corberi , Eugenio Lippiello , Paolo Politi

In this paper we suggest a consistent approach to derivation of generalized Fokker-Planck equation (GFPE) for Gaussian non-Markovian processes with stationary increments. This approach allows us to construct the probability density function…

Statistical Mechanics · Physics 2011-07-06 O. Yu. Sliusarenko

Combining the results of [14] and [10], the trend to equilibrium in large time is studied for a large particle system associated to a Vlasov-Fokker-Planck equation. Under some conditions (that allow non-convex confining potentials) the…

Probability · Mathematics 2021-11-17 Arnaud Guillin , Pierre Monmarché

The optimization of the usual entropy $S_1[p]=-\int du p(u) ln p(u)$ under appropriate constraints is closely related to the Gaussian form of the exact time-dependent solution of the Fokker-Planck equation describing an important class of…

Condensed Matter · Physics 2009-10-28 Constantino Tsallis , Dirk Jan Bukman

We show that, in conserved-mass transport processes, the steady-state distribution of mass in a subsystem is uniquely determined from the functional dependence of variance of the subsystem mass on its mean, provided that joint mass…

Statistical Mechanics · Physics 2014-03-17 Sayani Chatterjee , Punyabrata Pradhan , P. K. Mohanty

This contribution presents a derivation of the steady-state distribution of velocities and distances of vehicles in freeway traffic which has been suggested for the evaluation of interaction potentials among vehicles (see preprint…

Statistical Mechanics · Physics 2007-05-23 Dirk Helbing , Martin Treiber

The present Letter, deals with the statistical theory [Phys. Rev. E {\bf 66}, 056125 (2002) and Phys. Rev E {\bf 72}, 036108 (2005)], which predicts the probability distribution $p(E) \propto \exp_{\kappa} (-I)$, where, $I \propto \beta E…

Statistical Mechanics · Physics 2011-10-19 G. Kaniadakis