Displaying 61 – 80 of 307

Showing per page

Conditional distributions, exchangeable particle systems, and stochastic partial differential equations

Dan Crisan, Thomas G. Kurtz, Yoonjung Lee (2014)

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

Stochastic partial differential equations (SPDEs) whose solutions are probability-measure-valued processes are considered. Measure-valued processes of this type arise naturally as de Finetti measures of infinite exchangeable systems of particles and as the solutions for filtering problems. In particular, we consider a model of asset price determination by an infinite collection of competing traders. Each trader’s valuations of the assets are given by the solution of a stochastic differential equation,...

Density in small time for Lévy processes

Jean Picard (2010)

ESAIM: Probability and Statistics

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 cannot...

Deterministic Chaos vs. Stochastic Fluctuation in an Eco-epidemic Model

P.S. Mandal, M. Banerjee (2012)

Mathematical Modelling of Natural Phenomena

An eco-epidemiological model of susceptible Tilapia fish, infected Tilapia fish and Pelicans is investigated by several author based upon the work initiated by Chattopadhyay and Bairagi (Ecol. Model., 136, 103–112, 2001). In this paper, we investigate the dynamics of the same model by considering different parameters involved with the model as bifurcation parameters in details. Considering the intrinsic growth rate of susceptible Tilapia fish as bifurcation parameter, we demonstrate the period doubling...

Deviation bounds for additive functionals of Markov processes

Patrick Cattiaux, Arnaud Guillin (2008)

ESAIM: Probability and Statistics

In this paper we derive non asymptotic deviation bounds for ν ( | 1 t 0 t V ( X s ) d s - V d μ | R ) where X is a μ stationary and ergodic Markov process and V is some μ integrable function. These bounds are obtained under various moments assumptions for V , and various regularity assumptions for μ . Regularity means here that μ may satisfy various functional inequalities (F-Sobolev, generalized Poincaré etc.).

deviation bounds for additive functionals of markov processes

Patrick Cattiaux, Arnaud Guillin (2007)

ESAIM: Probability and Statistics

In this paper we derive non asymptotic deviation bounds for ν ( | 1 t 0 t V ( X s ) d s - V d μ | R ) where X is a μ stationary and ergodic Markov process and V is some μ integrable function. These bounds are obtained under various moments assumptions for V, and various regularity assumptions for μ. Regularity means here that μ may satisfy various functional inequalities (F-Sobolev, generalized Poincaré etc.).

Dislocation measure of the fragmentation of a general Lévy tree

Guillaume Voisin (2011)

ESAIM: Probability and Statistics

Given a general critical or sub-critical branching mechanism and its associated Lévy continuum random tree, we consider a pruning procedure on this tree using a Poisson snake. It defines a fragmentation process on the tree. We compute the family of dislocation measures associated with this fragmentation. This work generalizes the work made for a Brownian tree [R. Abraham and L. Serlet, Elect. J. Probab. 7 (2002) 1–15] and for a tree without Brownian part [R. Abraham and J.-F. Delmas, Probab. Th....

Dislocation measure of the fragmentation of a general Lévy tree

Guillaume Voisin (2012)

ESAIM: Probability and Statistics

Given a general critical or sub-critical branching mechanism and its associated Lévy continuum random tree, we consider a pruning procedure on this tree using a Poisson snake. It defines a fragmentation process on the tree. We compute the family of dislocation measures associated with this fragmentation. This work generalizes the work made for a Brownian tree [R. Abraham and L. Serlet, Elect. J. Probab.7 (2002) 1–15] and for a tree without Brownian part [R. Abraham and J.-F. Delmas, Probab. Th....

Currently displaying 61 – 80 of 307