Linear diffusion with stationary switching regime

Xavier Guyon; Serge Iovleff; Jian-Feng Yao

Displaying similar documents to “Linear diffusion with stationary switching regime”

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...

Transience, recurrence and speed of diffusions with a non-markovian two-phase “use it or lose it” drift

Ross G. Pinsky (2014)

Annales de l'I.H.P. Probabilités et statistiques

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We investigate the transience/recurrence of a non-Markovian, one-dimensional diffusion process which consists of a Brownian motion with a non-anticipating drift that has two phases – a transient to $+ \infty$ mode which is activated when the diffusion is sufficiently near its running maximum, and a recurrent mode which is activated otherwise. We also consider the speed of a diffusion with a two-phase drift, where the drift is equal to a certain non-negative constant when the diffusion is sufficiently...

Regularity of stopping times of diffusion processes in Besov spaces

Xicheng Zhang (2002)

Studia Mathematica

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We prove that the exit times of diffusion processes from a bounded open set Ω almost surely belong to the Besov space $B_{p, q}^{α} (Ω)$ provided that pα < 1 and 1 ≤ q < ∞.

Transformation of Markov processes by multiplicative functionals

K. Ito, S. Watanabe (1965)

Annales de l'institut Fourier

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Il s’agit du développement détaillé de l’idée que l’un des auteurs, K. Itô, a présentée au Colloque de théorie du potentiel. Étant donné une fonctionnelle multiplicative $α$ , d’un processus de Hunt $X_{t}$ , on construit le $α$ -sous processus de $X_{t}$ . La section 1 donne un aperçu historique et une idée sommaire de la construction. La section 2 est consacrée au théorème de factorisation pour super martingale positive, d’après quoi on prouve qu’une fonctionnelle multiplicative super régulière...

Long time behaviour and stationary regime of memory gradient diffusions

Sébastien Gadat, Fabien Panloup (2014)

Annales de l'I.H.P. Probabilités et statistiques

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In this paper, we are interested in a diffusion process based on a gradient descent. The process is non Markov and has a memory term which is built as a weighted average of the drift term all along the past of the trajectory. For this type of diffusion, we study the long time behaviour of the process in terms of the memory. We exhibit some conditions for the long-time stability of the dynamical system and then provide, when stable, some convergence properties of the occupation measures...

Gaussian approximation for functionals of Gibbs particle processes

Daniela Flimmel, Viktor Beneš (2018)

Kybernetika

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In the paper asymptotic properties of functionals of stationary Gibbs particle processes are derived. Two known techniques from the point process theory in the Euclidean space $ℝ^{d}$ are extended to the space of compact sets on $ℝ^{d}$ equipped with the Hausdorff metric. First, conditions for the existence of the stationary Gibbs point process with given conditional intensity have been simplified recently. Secondly, the Malliavin-Stein method was applied to the estimation of Wasserstein distance...

Two stationarity conditions in the $G I / r_{0} / M / r_{1}$ dam

M. Jankiewicz (1988)

Applicationes Mathematicae

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Estimates of stability of Markov control processes with unbounded costs

Evgueni I. Gordienko, Francisco Salem-Silva (2000)

Kybernetika

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For a discrete-time Markov control process with the transition probability $p$ , we compare the total discounted costs $V_{β}$ $(π_{β})$ and $V_{β} ({\tilde{π}}_{β})$ , when applying the optimal control policy $π_{β}$ and its approximation ${\tilde{π}}_{β}$ . The policy ${\tilde{π}}_{β}$ is optimal for an approximating process with the transition probability $\tilde{p}$ . A cost per stage for considered processes can be unbounded. Under certain ergodicity assumptions we establish the upper bound for the relative stability index $[V_{β} ({\tilde{π}}_{β}) - V_{β} (π_{β})] / V_{β} (π_{β})$ . This bound does not depend...

An estimator for parameters of a nonlinear nonnegative multidimensional AR(1) process

Jiří Anděl (1998)

Applications of Mathematics

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Let $𝕖_{t} = {(e_{t 1}, \dots, e_{t p})}^{'}$ be a $p$ -dimensional nonnegative strict white noise with finite second moments. Let $h_{i j} (x)$ be nondecreasing functions from $[0, \infty)$ onto $[0, \infty)$ such that $h_{i j} (x) \leq x$ for $i, j = 1, \dots, p$ . Let $𝕌 = (u_{i j})$ be a $p \times p$ matrix with nonnegative elements having all its roots inside the unit circle. Define a process $𝕏_{t} = {(X_{t 1}, \dots, X_{t p})}^{'}$ by $X_{t j} = u_{j 1} h_{1 j} (X_{t - 1, 1}) + \dots + u_{j p} h_{p j} (X_{t - 1, p}) + e_{t j}$ for $j = 1, \dots, p$ . A method for estimating $𝕌$ from a realization $𝕏_{1}, \dots, 𝕏_{n}$ is proposed. It is proved that the estimators are strongly consistent.