Displaying similar documents to “Microscopic concavity and fluctuation bounds in a class of deposition processes”

Limits of determinantal processes near a tacnode

Alexei Borodin, Maurice Duits (2011)

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

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We study a Markov process on a system of interlacing particles. At large times the particles fill a domain that depends on a parameter > 0. The domain has two cusps, one pointing up and one pointing down. In the limit ↓ 0 the cusps touch, thus forming a tacnode. The main result of the paper is a derivation of the local correlation kernel around the tacnode in the transition regime ↓ 0. We also prove that the local process interpolates between the Pearcey process and the GUE...

Branching Stochastic Processes: History, Theory, Applications Разклоняващи се стохастични процеси: история, теория, приложения

Mitov, Kosto (2011)

Union of Bulgarian Mathematicians

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Косто В. Митов - Разклоняващите се стохастични процеси са модели на популационната динамика на обекти, които имат случайно време на живот и произвеждат потомци в съответствие с дадени вероятностни закони. Типични примери са ядрените реакции, клетъчната пролиферация, биологичното размножаване, някои химични реакции, икономически и финансови явления. В този обзор сме се опитали да представим съвсем накратко някои от най-важните моменти и факти от историята, теорията и приложенията на...

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.

Refracted Lévy processes

A. E. Kyprianou, R. L. Loeffen (2010)

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

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Motivated by classical considerations from risk theory, we investigate boundary crossing problems for refracted Lévy processes. The latter is a Lévy process whose dynamics change by subtracting off a fixed linear drift (of suitable size) whenever the aggregate process is above a pre-specified level. More formally, whenever it exists, a refracted Lévy process is described by the unique strong solution to the stochastic differential equation d =− { ...

On suprema of Lévy processes and application in risk theory

Renming Song, Zoran Vondraček (2008)

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

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Let =− where is a general one-dimensional Lévy process and an independent subordinator. Consider the times when a new supremum of is reached by a jump of the subordinator . We give a necessary and sufficient condition in order for such times to be discrete. When this is the case and drifts to −∞, we decompose the absolute supremum of at these times, and derive a Pollaczek–Hinchin-type formula for the distribution function of the supremum.

Couplings, attractiveness and hydrodynamics for conservative particle systems

Thierry Gobron, Ellen Saada (2010)

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

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Attractiveness is a fundamental tool to study interacting particle systems and the basic coupling construction is a usual route to prove this property, as for instance in simple exclusion. The derived markovian coupled process ( , )≥0 satisfies: (A) if 0≤0 (coordinate-wise), then for all ≥0, ≤ a.s. In this paper, we consider generalized misanthrope models which are conservative particle systems on ℤ such that, in each transition,...