Related papers: SDE in Random Population Growth
The approximative theorems of incomplete Riemann-Stieltjes sums of Ito stochastic integral, mean square integral and Stratonovich stochastic integral with respect to Brownian motion are investigated. Some sufficient conditions of incomplete…
This paper provides a new characterization of the stochastic invariance of a closed subset of R^d with respect to a diffusion. We extend the well-known inward pointing Stratonovich drift condition to the case where the diffusion matrix can…
We review the formulation of the stochastic Burgers equation as a martingale problem. One way of understanding the difficulty in making sense of the equation is to note that it is a stochastic PDE with distributional drift, so we first…
Stochasticity can play an important role in the dynamics of biologically relevant populations. These span a broad range of scales: from intra-cellular populations of molecules to population of cells and then to groups of plants, animals and…
This work proposes and analyzes a family of spatially inhomogeneous epidemic models. This is our first effort to use stochastic partial differential equations (SPDEs) to model epidemic dynamics with spatial variations and environmental…
Motivated by the lack of a suitable constructive framework for analyzing popular stochastic models of Systems Biology, we devise conditions for existence and uniqueness of solutions to certain jump stochastic differential equations (SDEs).…
Stochastic multiplicative dynamics characterize many complex natural phenomena such as selection and mutation in evolving populations, and the generation and distribution of wealth within social systems. Population heterogeneity in…
Random population dynamics with catastrophes (events pertaining to possible elimination of a large portion of the population) has a long history in the mathematical literature. In this paper we study an ergodic model for random population…
It is well known, mainly because of the work of Kurtz, that density dependent Markov chains can be approximated by sets of ordinary differential equations (ODEs) when their indexing parameter grows very large. This approximation cannot…
In recent years, stochastic dominance for independent and identically distributed (iid) infinite-mean random variables has received considerable attention. The literature has identified several classes of distributions of nonnegative random…
Population dynamics and in particular microbial population dynamics, though they are complex but also intrinsically discrete and random, are conventionally represented as deterministic differential equations systems. We propose to revisit…
We study a numerical method to compute probability density functions of solutions of stochastic differential equations. The method is sometimes called the numerical path integration method and has been shown to be fast and accurate in…
We consider consistent dynamics for non-intersecting birth and death chains, originating from dualities of stochastic coalescing flows and one dimensional orthogonal polynomials. As corollaries, we obtain unified and simple probabilistic…
In this paper we introduce a class of stochastic population models based on "patch dynamics". The size of the patch may be varied, and this allows one to quantify the departures of these stochastic models from various mean field theories,…
We present Extended Riemannian Stochastic Derivative-Free Optimization (Extended RSDFO), a novel population-based stochastic optimization algorithm on Riemannian manifolds that addresses the locality and implicit assumptions of manifold…
In recent years there has been a growing interest in the study of the dynamics of stochastic populations. A key question in population biology is to understand the conditions under which populations coexist or go extinct. Theoretical and…
Stochastic expansion-based methods of uncertainty quantification, such as polynomial chaos and separated representations, require basis functions orthogonal with respect to the density of random inputs. Many modern engineering problems…
Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the…
A stochastic calculus is given for processes described by stochastic integrals with respect to fractional Brownian motions and Rosenblatt processes somewhat analogous to the stochastic calculus for It\^{o} processes. These processes for…
This article proposes a new approximation scheme for quadratic-growth BSDEs in a Markovian setting by connecting a series of semi-analytic asymptotic expansions applied to short-time intervals. Although there remains a condition which needs…