Displaying similar documents to “Long time behaviour and stationary regime of memory gradient diffusions”

Sur quelques algorithmes récursifs pour les probabilités numériques

Gilles Pagès (2010)

ESAIM: Probability and Statistics

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The aim of this paper is to take an in-depth look at the long time behaviour of some continuous time Markovian dynamical systems and at its numerical analysis. We first propose a short overview of the main ergodicity properties of time continuous homogeneous Markov processes (stability, positive recurrence). The basic tool is a Lyapunov function. Then, we investigate if these properties still hold for the time discretization of these processes, either with constant or decreasing...

Probability and quanta: why back to Nelson?

Piotr Garbaczewski (1998)

Banach Center Publications

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We establish circumstances under which the dispersion of passive contaminants in a forced flow can be consistently interpreted as a Markovian diffusion process.

Linear diffusion with stationary switching regime

Xavier Guyon, Serge Iovleff, Jian-Feng Yao (2004)

ESAIM: Probability and Statistics

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Let Y be a Ornstein–Uhlenbeck diffusion governed by a stationary and ergodic process X : d Y t = a ( X t ) Y t d t + σ ( X t ) d W t , Y 0 = y 0 . We establish that under the condition α = E μ ( a ( X 0 ) ) < 0 with μ the stationary distribution of the regime process X , the diffusion Y is ergodic. We also consider conditions for the existence of moments for the invariant law of Y when X is a Markov jump process having a finite number of states. Using results on random difference equations on one hand and the fact that conditionally to X , Y is gaussian on the other...

A stochastic symbiosis model with degenerate diffusion process

Urszula Skwara (2010)

Annales Polonici Mathematici

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We present a model of symbiosis given by a system of stochastic differential equations. We consider a situation when the same factor influences both populations or only one population is stochastically perturbed. We analyse the long-time behaviour of the solutions and prove the asymptoptic stability of the system.

Long memory and self-similar processes

Gennady Samorodnitsky (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

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This paper is a survey of both classical and new results and ideas on long memory, scaling and self-similarity, both in the light-tailed and heavy-tailed cases.

Stochastic differential equation driven by a pure-birth process

Marta Tyran-Kamińska (2002)

Annales Polonici Mathematici

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A generalization of the Poisson driven stochastic differential equation is considered. A sufficient condition for asymptotic stability of a discrete time-nonhomogeneous Markov process is proved.

From convergence of operator semigroups to gene expression, and back again

Adam Bobrowski (2008)

Banach Center Publications

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The subject of the paper is reciprocal influence of pure mathematics and applied sciences. We illustrate the idea by giving a review of mathematical results obtained recently, related to the model of stochastic gene expression due to Lipniacki et al. [38]. In this model, featuring mRNA and protein levels, and gene activity, the stochastic part of processes involved in gene expression is distinguished from the part that seems to be mostly deterministic, and the dynamics is expressed by...