相关论文: Generalized Fokker-Planck equation and its solutio…

For stochastic systems with discrete time delay, the Fokker-Planck equation (FPE) of the one-time probability density function (PDF) does not provide a complete, self-contained probabilistic description. It explicitly involves the two-time…

We derive the exact evolution equation for the probability density function of particle displacements generated by arbitrary Gaussian velocity processes, when neither Markovianity and nor stationarity are assumed. Starting from the…

Many complex phenomena occurring in physics,chemistry, biology, finance, etc. can be reduced, by some projection process, to a 1-d stochastic Differential Equation (SDE) for the variable of interest. Typically, this SDE is both non-linear…

We present a simple thermodynamically consistent method for solving time-dependent Fokker--Planck equations (FPE) for over-damped stochastic processes, also known as Smoluchowski equations. It yields both transition and steady-state…

The classical Fokker-Planck equation (FPE) is a key tool in physics for describing systems influenced by drag forces and Gaussian noise, with applications spanning multiple fields. We consider the fractional Fokker-Planck equation (FFPE),…

The relaxation to equilibrium in many systems which show strange kinetics is described by fractional Fokker-Planck equations (FFPEs). These can be considered as phenomenological equations of linear nonequilibrium theory. We show that the…

The probabilistic characterization of non-Markovian responses to nonlinear dynamical systems under colored excitation is an important issue, arising in many applications. Extending the Fokker-Planck-Kolmogorov equation, governing the…

The Fokker-Planck equations (FPEs) for stochastic systems driven by additive symmetric $\alpha$-stable noises may not adequately describe the time evolution for the probability densities of solution paths in some practical applications,…

In this work, we propose adaptive deep learning approaches based on normalizing flows for solving fractional Fokker-Planck equations (FPEs). The solution of a FPE is a probability density function (PDF). Traditional mesh-based methods are…

Solving the Fokker-Planck equation for high-dimensional complex turbulent dynamical systems is an important and practical issue. However, most traditional methods suffer from the curse of dimensionality and have difficulties in capturing…

The Fokker-Planck equations describe time evolution of probability densities of stochastic dynamical systems and are thus widely used to quantify random phenomena such as uncertainty propagation. For dynamical systems driven by non-Gaussian…

This article presents a rigorous analysis for efficient statistically accurate algorithms for solving the Fokker-Planck equations associated with high-dimensional nonlinear turbulent dynamical systems with conditional Gaussian structures.…

The Fokker-Planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by Gaussian noises. In this paper, we derive a Fractional Fokker--Planck equation for the probability distribution of…

In this study, we propose a new method that is useful for estimating unknown parameter values of stochastic differential equation (SDE) models, based on probability density function (PDF) data measured from random dynamical systems. As our…

We investigate the dynamics of an inertial active Ornstein-Uhlenbeck particle suspended in a non-Markovian environment. The particle is additionally subjected to external forces, such as harmonic confinement and a magnetic field. Motivated…

The Fokker-Planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by Gaussian noises. However, there are both theoretical and empirical reasons to consider similar equations driven by…

Efficiently solving the Fokker-Planck equation (FPE) is crucial for understanding the probabilistic evolution of stochastic particles in dynamical systems, however, analytical solutions or density functions are only attainable in specific…

The fractional Fokker-Planck equation (FFPE) [R. Metzler, E. Barkai, J. Klafter, Phys. Rev. Lett., 82, 3563 (1999)] describes an anomalous sub diffusive behavior of a particle in an external force field. In this paper we present the…

General Stochastic Hybrid Systems (GSHS) have been formulated to represent various types of uncertainties in hybrid dynamical systems. In this paper, we propose computational techniques for Bayesian estimation of GSHS. In particular, the…

We show that the increments of generalized Wiener process, useful to describe non-Gaussian white noise sources, have the properties of infinitely divisible random processes. Using functional approach and the new correlation formula for…