Stability of stochastic differential equations with Markovian switching has recently been discussed by many authors, for example, Basak et al. (J. Math. Anal. Appl. 202 (1996) 604), Ji and Chizeck (IEEE Trans. Automat. Control 35 (1990) 777), Mariton (Jump Linear System in Automatic Control,...

We construct a catalytic super process X (measure-valued spatial branching process) where the local branching rate is governed by an additive functional A of the motion process. These processes have been investigated before but under restrictive assumptions on A. Here we do not even need...

We study the Cauchy-Dirichlet problem for a second-order linear parabolic stochastic differential equation in the half-space with a zero-order noise term driven by a cylindrical Brownian motion. Considering its solution as a function with values in a probability space and using the methods of...

In this paper we study necessary and sufficient conditions for the equivalence of Volterra Gaussian processes. Though this topic has already been studied in the literature, we provide new proofs, precisions and new theorems. We also give some examples of equivalent Volterra processes all related...

We consider the lifetime consumption-portfolio problem in a competitive securities market with essentially arbitrary continuous price dynamics, and convex trading constraints (e.g., incomplete markets and short-sale constraints). Abstract first-order conditions of optimality are derived, based...

We consider the Euler approximation of stochastic differential equations (SDEs) driven by Lévy processes in the case where we cannot simulate the increments of the driving process exactly. In some cases, where the driving process Y is a subordinated stable process, i.e., Y=Z(V) with V a...

We study the long-time behavior of the solution u(t,x) of a Cauchy problem for the one-dimensional heat equation with constant drift and random potential in the quenched setting: . The initial function is compactly supported. For bounded stationary ergodic potential [xi], we show that u is...

A dynamic programming principle is derived for a discrete time Markov control process taking values in a finite dimensional space, with ergodic cost and partial observations. This uses the embedding of the process into another for which an accessible atom exists and hence a coupling argument can...

Consider a population model in which there are N individuals in each generation. One can obtain a coalescent tree by sampling n individuals from the current generation and following their ancestral lines backwards in time. It is well-known that under certain conditions on the joint distribution...

In this paper, we investigate the rate of convergence for general d-dimensional stochastic approximation procedures and present an explicit expression for the asymptotic bounds in the law of the iterated logarithm.