Displaying similar documents to “Davis-type inequalities for a number of diffusion processes.”

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...

Density in small time for Lévy processes

Jean Picard (2010)

ESAIM: Probability and Statistics

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The density of real-valued Lévy processes is studied in small time under the assumption that the process has many small jumps. We prove that the real line can be divided into three subsets on which the density is smaller and smaller: the set of points that the process can reach with a finite number of jumps (Δ-accessible points); the set of points that the process can reach with an infinite number of jumps (asymptotically Δ-accessible points); and the set of points that the process...

Lévy Processes, Saltatory Foraging, and Superdiffusion

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

Mathematical Modelling of Natural Phenomena

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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...

Continuous-time multitype branching processes conditioned on very late extinction

Sophie Pénisson (2011)

ESAIM: Probability and Statistics

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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.