Displaying similar documents to “Intertwining of 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

Similarity:

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 + ∞ 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...

Lévy Processes, Saltatory Foraging, and Superdiffusion

J. F. Burrow, P. D. Baxter, J. W. Pitchford (2008)

Mathematical Modelling of Natural Phenomena

Similarity:

It is well established that resource variability generated by spatial patchiness and turbulence is an important influence on the growth and recruitment of planktonic fish larvae. Empirical data show fractal-like prey distributions, and simulations indicate that scale-invariant foraging strategies may be optimal. Here we show how larval growth and recruitment in a turbulent environment can be formulated as a hitting time problem for a jump-diffusion process. We present two theoretical...

Linear diffusion with stationary switching regime

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

ESAIM: Probability and Statistics

Similarity:

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...

Asymptotics for conservation laws involving Lévy diffusion generators

Piotr Biler, Grzegorz Karch, Wojbor A. Woyczyński (2001)

Studia Mathematica

Similarity:

Let -ℒ be the generator of a Lévy semigroup on L¹(ℝⁿ) and f: ℝ → ℝⁿ be a nonlinearity. We study the large time asymptotic behavior of solutions of the nonlocal and nonlinear equations uₜ + ℒu + ∇·f(u) = 0, analyzing their L p -decay and two terms of their asymptotics. These equations appear as models of physical phenomena that involve anomalous diffusions such as Lévy flights.

Transformation of Markov processes by multiplicative functionals

K. Ito, S. Watanabe (1965)

Annales de l'institut Fourier

Similarity:

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...

Probability and quanta: why back to Nelson?

Piotr Garbaczewski (1998)

Banach Center Publications

Similarity:

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

Continuous-time multitype branching processes conditioned on very late extinction

Sophie Pénisson (2011)

ESAIM: Probability and Statistics

Similarity:

Multitype branching processes and Feller diffusion processes are conditioned on very late extinction. The conditioned laws are expressed as Doob -transforms of the unconditioned laws, and an interpretation of the conditioned paths for the branching process is given, the immortal particle. We study different limits for the conditioned process (increasing delay of extinction, long-time behavior, scaling limit) and provide an exhaustive list of exchangeability results.

Steady states for a fragmentation equation with size diffusion

Philippe Laurençot (2004)

Banach Center Publications

Similarity:

The existence of a one-parameter family of stationary solutions to a fragmentation equation with size diffusion is established. The proof combines a fixed point argument and compactness techniques.

Attractors for stochastic reaction-diffusion equation with additive homogeneous noise

Jakub Slavík (2021)

Czechoslovak Mathematical Journal

Similarity:

We study the asymptotic behaviour of solutions of a reaction-diffusion equation in the whole space ℝ d driven by a spatially homogeneous Wiener process with finite spectral measure. The existence of a random attractor is established for initial data in suitable weighted L 2 -space in any dimension, which complements the result from P. W. Bates, K. Lu, and B. Wang (2013). Asymptotic compactness is obtained using elements of the method of short trajectories.

Remarks on balanced norm error estimates for systems of reaction-diffusion equations

Hans-Goerg Roos (2018)

Applications of Mathematics

Similarity:

Error estimates of finite element methods for reaction-diffusion problems are often realized in the related energy norm. In the singularly perturbed case, however, this norm is not adequate. A different scaling of the H 1 seminorm leads to a balanced norm which reflects the layer behavior correctly. We discuss the difficulties which arise for systems of reaction-diffusion problems.