相关论文: Exact Solution of the Multi-Allelic Diffusion Mode…

We present a numerical method to accurately simulate particle size distributions within the formalism of rate equation cluster dynamics. This method is based on a discretization of the associated Fokker-Planck equation. We show that…

We provide a detailed description of the structure of the transition probabilities and of the hitting distributions of boundary components of a manifold with corners for a degenerate strong Markov process arising in population genetics. The…

When comparing two distributions, it is often helpful to learn at which quantiles or values there is a statistically significant difference. This provides more information than the binary "reject" or "do not reject" decision of a global…

The Smoluchowski equation with a time dependent sink term is solved exactly. In this method by knowing the probability distribution at the origin P(0,s), one may derive the probability distribution at all positions i.e., P(x,s). Further the…

We consider a formulation of initial problem for Kolmogorov equation that corresponds a localized source of particles to be scattered by medium with given scattering amplitude density (scattering indicatrix). The multiple scattering…

In this paper, we construct the fundamental solution to a degenerate diffusion of Kolmogorov type and develop a time-discrete variational scheme for its adjoint equation. The so-called mean squared derivative cost function plays a crucial…

The rigorous linking of exact stochastic models to mean-field approximations is studied. Starting from the differential equation point of view the stochastic model is identified by its Kolmogorov equations, which is a system of linear ODEs…

A discrete time branching process where the offspring distribution is generation-dependent, and the number of reproductive individuals is controlled by a random mechanism is considered. This model is a Markov chain but, in general, the…

We develop a new method to uniquely solve a large class of heat equations, so-called Kolmogorov equations in infinitely many variables. The equations are analyzed in spaces of sequentially weakly continuous functions weighted by proper…

The mean fixation time of a deleterious mutant allele is studied beyond the diffusion approximation. As in Kimura's classical work [M. Kimura, Proc. Natl. Acad. Sci. U.S.A. Vol.77, 522 (1980)], that was motivated by the problem of fixation…

In this paper we study the numerical method for approximating the random periodic solution of semiliear stochastic evolution equations. The main challenge lies in proving a convergence over an infinite time horizon while simulating…

The exact solution of the asymmetric exclusion problem and several of its generalizations is obtained by a matrix product {\it ansatz}. Due to the similarity of the master equation and the Schr\"odinger equation at imaginary times the…

We introduce a multi-allele Wright-Fisher model with non-recurrent, reversible mutation and directional selection. In this setting, the allele frequencies at a single locus track the path of a hybrid jump-diffusion process with state space…

We study qualitative properties of solutions to double divergence form elliptic equations (or stationary Kolmogorov equations) on~$\mathbb{R}^d$. It is shown that the Harnack inequality holds for nonnegative solutions if the diffusion…

We develop a finite difference scheme based on a grid staggered by flux points and solution points to solve Fokker-Planck equations with drift-admitting jumps. To satisfy the matching conditions at the jumps, i.e., the continuities of the…

The two-dimensional generalization of the Polyelectolite model of DNA is proposed. It is reduced to the boundary problem for nonlinear completely integrable equation $\sh$-Gordon. In the linearisible version the exact solution is…

In this paper, we explore the solvability and the optimal control problem for a compartmental model based on reaction-diffusion partial differential equations describing a transmissible disease. The nonlinear model takes into account the…

In this paper, we study numerical methods for the homogenization of linear second-order elliptic equations in nondivergence-form with periodic diffusion coefficients and large drift terms. Upon noting that the effective diffusion matrix can…

This paper studies three ways to construct a nonhomogeneous jump Markov process: (i) via a compensator of the random measure of a multivariate point process, (ii) as a minimal solution of the backward Kolmogorov equation, and (iii) as a…

Statistics of molecular random walks in a fluid is considered with the help of the Bogolyubov equation for generating functional of distribution functions. An invariance group of solutions to this equation as functions of the fluid density…