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We investigate the long-time evolution of branching diffusion processes (starting with a single particle) in inhomogeneous media. The qualitative behavior of the processes depends on the intensity of ...
In this paper, we establish several gradient estimates for the positive solution of Porous Medium Equations (PMEs) and Fast Diffusion Equations (FDEs). Our proof is probabilistic and uses martingale t...
In this article, we address the dynamics and bifurcations of a wide class of stochastic differential equations around singular points where both the drift and diffusion functions vanish. We apply thes...
For a minimal diffusion process on $ (a,b) $, any possible extension of it to a standard process on $ [a,b] $ is characterized by the characteristic measures of excursions away from the boundary point...
Abstract: Homogenization of a stochastic nonlinear reaction-diffusion equation with a large non- linear term is considered. Under a general Besicovitch almost periodicity assumption on the coefficient...
Abstract: This paper studies diffusion processes constrained to the positive orthant, and investigates changes in the steady-state distribution of such diffusions under infinitesimal changes in the dr...
Abstract: We consider diffusion processes x_{t} on the unit interval. Doob-transformation techniques consist of a selection of x_{t}-paths procedure. The law of the transformed process is the one of a...
Abstract: We investigate the long-time evolution of branching diffusion processes (starting with a finite number of particles) in inhomogeneous media. The qualitative behavior of the processes depends...
Abstract: By using the Malliavin calculus and solving a control problem, Bismut type derivative formulae are established for a class of degenerate diffusion semigroups with non-linear drifts. As appli...
Abstract: A linear Boltzmann equation is interpreted as the forward equation for the probability density of a Markov process (K(t), i(t), Y(t)), where (K(t), i(t)) is an autonomous reversible jump pro...
We consider the Fast Di usion Equation ut = um posed in a bounded smooth domain  Rd with homogeneous Dirichlet conditions; the exponent range is ms = (d 􀀀 2)+=(d + 2) < m < 1.It is known...
In this article we extend earlier work on the jump-diffusion risk-sensitive asset management problem by allowing for jumps in both the factor process and the asset prices as well as stochastic volatil...
Mandatory emission trading schemes are being established around the world. Participants of such market schemes are always exposed to risks. This leads to the creation of an accompanying market for emi...
We propose a new method to construct an isotropic cellular automaton corresponding to a reaction-diffusion equation. The method consists of replacing the diffusion term and the reaction term of the re...

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