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.

Intertwining of the Wright-Fisher diffusion

Tobiáš Hudec (2017)

Kybernetika

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It is known that the time until a birth and death process reaches a certain level is distributed as a sum of independent exponential random variables. Diaconis, Miclo and Swart gave a probabilistic proof of this fact by coupling the birth and death process with a pure birth process such that the two processes reach the given level at the same time. Their coupling is of a special type called intertwining of Markov processes. We apply this technique to couple the Wright-Fisher diffusion...

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.