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

This paper investigates the probability distribution of solutions to McKean--Vlasov stochastic differential equations driven by fractional Brownian motion with Hurst parameter H>1/2. Our main contribution is the derivation of the associated…

We propose a prescription based on the Fokker-Planck equation in the Stratonovich approach, with the diffusion coefficient dependent on temporal and spatial coordinates, for describing heat conduction by phonons in small structures. This…

We consider a Langevin equation with variable drift and diffusion coefficients separable in time and space and its corresponding Fokker-Planck equation in the Stratonovich approach. From this Fokker-Planck equation we obtain a class of…

Implicit particle filtering is a sequential Monte Carlo method for data assim- ilation, designed to keep the number of particles manageable by focussing attention on regions of large probability. These regions are found by min- imizing, for…

A large variety of microscopic or mesoscopic models lead to generic results that accommodate naturally within Boltzmann-Gibbs statistical mechanics (based on $S_1\equiv -k \int du p(u) \ln p(u)$). Similarly, other classes of models point…

We investigate a subdiffusive, fractional Fokker-Planck dynamics occurring in time-varying potential landscapes and thereby disclose the failure of the fractional Fokker-Planck equation (FFPE) in its commonly used form when generalized in…

We investigate the regularity of the law of Wong-Zakai-type approximations for It\^o stochastic differential equations. These approximations solve random differential equations where the diffusion coefficient is Wick-multiplied by the…

It is well known that the nonlinear filtering problem has important applications in both military and civil industries. The central problem of nonlinear filtering is to solve the Duncan-Mortensen-Zakai (DMZ) equation in real time and in a…

This work is devoted to the study of the Fokker--Planck equation for a stochastic heat equation with an additive $Q$-Wiener noise and non-homogeneous boundary conditions. We explicitly construct the probability density function and…

Solving inverse problems without the use of derivatives or adjoints of the forward model is highly desirable in many applications arising in science and engineering. In this paper, we propose a new version of such a methodology, a framework…

We introduce a weighted particle representation for the solution of the filtering problem based on a suitably chosen variation of the classical de Finetti theorem. This representation has important theoretical and numerical applications. In…

This paper proposes a probabilistic approach to the problem of intrinsic filtering of a system on a matrix Lie group with invariance properties. The problem of an invariant continuous-time model with discrete-time measurements is cast into…

We present a model of diffusion in heterogeneous environment, which qualitatively reflects the transport properties of a polymeric membrane with carbon nanotubes. We derived Fokker-Planck equation from system of stochastic equations,…

The Fokker-Planck Equation (FPE) is a fundamental tool for the investigation of kinematic aspects of a wide range of systems. For systems governed by the non-additive entropy $S_q$, the Plastino-Plastino Equation (PPE) is the correct…

This article considers the application of particle filtering to continuous-discrete optimal filtering problems, where the system model is a stochastic differential equation, and noisy measurements of the system are obtained at discrete…

We present the path integral formulation of a broad class of generalized diffusion processes. Employing the path integral we derive exact expressions for the path probability densities and joint probability distributions for the class of…

This article studies a Fokker-Planck type equation of fractional diffusion with conservative drift $\partial$f/$\partial$t = $\Delta$^($\alpha$/2) f + div(Ef), where $\Delta$^($\alpha$/2) denotes the fractional Laplacian and E is a…

This paper derives Langevin equations for an optical cavity where the dominant nonlinearity arises from free-carrier dispersion. We define a generalized Wigner function, compute a Fokker-Planck equation that approximates the master…

We solve a physically significant extension of a classic problem in the theory of diffusion, namely the Ornstein-Uhlenbeck process [G. E. Ornstein and L. S. Uhlenbeck, Phys. Rev. 36, 823, (1930)]. Our generalised Ornstein-Uhlenbeck systems…

The Fokker-Planck equation is a partial differential equation that describes the evolution of a probability distribution over time. It is used to model a wide range of physical and biological phenomena, such as diffusion, chemical…