相关论文: Universal Nonlinear Filtering Using Feynman Path I…

This paper analyzes a full discretization of a three-dimensional stochastic Allen-Cahn equation with multiplicative noise. The discretization combines the Euler scheme for temporal approximation and the finite element method for spatial…

The existence and uniqueness of measure-valued solutions to stochastic nonlinear, non-local Fokker-Planck equations is proven. This type of stochastic PDE is shown to arise in the mean field limit of weakly interacting diffusions with…

The Langevin system subjected to non-Gaussian noise has been discussed, by using the second-order moment approach with two kinds of models for generating the noise. We have derived the effective differential equation (DE) for a variable…

This paper explores the use of a discrete singular convolution algorithm as a unified approach for numerical integration of the Fokker-Planck equation. The unified features of the discrete singular convolution algorithm are discussed. It is…

Kernel learning forward backward SDE filter is an iterative and adaptive meshfree approach to solve the nonlinear filtering problem. It builds from forward backward SDE for Fokker-Planker equation, which defines evolving density for the…

Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…

Many systems of partial differential equations have been proposed as simplified representations of complex collective behaviours in large networks of neurons. In this survey, we briefly discuss their derivations and then review the…

Efficient and accurate integration of stochastic (partial) differential equations with multiplicative noise can be obtained through a split-step scheme, which separates the integration of the deterministic part from that of the stochastic…

A Langevin equation with a special type of additive random source is considered. This random force presents a fractional order derivative of white noise, and leads to a power-law time behavior of the mean square displacement of a particle,…

We provide new regularity results for the solutions of the Kolmogorov equation associated to a SPDE with nonlinear diffusion coefficients and a Burgers type nonlinearity. This generalizes previous results in the simpler cases of additive or…

Feynman's path integral is herein generalized to the nonextensive canonical density matrix based on Tsallis entropy. This generalization is done in two ways by using unnormalized and normalized constraints. Firstly, we consider the path…

This paper considers the Fokker-Planck equation and path integral formulation of the fractional Ornstein-Uhlenbeck process parametrized by two indices. The effective Fokker-Planck equation of this process is derived from the associated…

We formulate Feynman path integral on a non commutative plane using coherent states. The propagator for a free particle exhibits UV cut-off induced by the parameter of non commutativity.

This paper is devoted to a fundamental solution of a nonlinear kinetic equation involving a porous medium or fast diffusion operator acting on velocities. Such a nonlinearity has interesting scaling properties, which result in a…

We obtain new exact classes of solutions for the nonlinear fractional Fokker-Planck-like equation partial_t rho = partial_x{D(x) partial^{mu -1}_x rho^{nu} - F(x) rho} by considering a diffusion coefficient D = D|x|^{-theta} (theta in R and…

We consider the problem of filtering dynamical systems, possibly stochastic, using observations of statistics. Thus, the computational task is to estimate a time-evolving density $\rho(v, t)$ given noisy observations of the true density…

A new Langevin equation with a field-dependent kernel is proposed to deal with bottomless systems within the framework of the stochastic quantization of Parisi and Wu. The corresponding Fokker-Planck equation is shown to be a diffusion-type…

McKean-Vlasov SDEs describe systems where the dynamics depend on the law of the process. The corresponding Fokker-Planck equation is a nonlinear, nonlocal PDE for the corresponding measure flow. In the presence of common noise and…

The exact solution of the Cauchy problem for a generalized "linear" vectorial Fokker-Planck equation is found using the disentangling techniques of R. Feynman and algebraic (operational) methods. This approach may be considered as a…

In this paper we consider the continuous--time nonlinear filtering problem, which has an infinite--dimensional solution in general, as proved by Chaleyat--Maurel and Michel. There are few examples of nonlinear systems for which the optimal…