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A backward particle interpretation of Feynman-Kac formulae

Pierre Del Moral, Arnaud Doucet, Sumeetpal S. Singh (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We design a particle interpretation of Feynman-Kac measures on path spaces based on a backward Markovian representation combined with a traditional mean field particle interpretation of the flow of their final time marginals. In contrast to traditional genealogical tree based models, these new particle algorithms can be used to compute normalized additive functionals “on-the-fly” as well as their limiting occupation measures with a given precision degree that does not depend on the final time horizon. We...

A branching-selection process related to censored Galton–Walton processes

Olivier Couronné, Lucas Gerin (2014)

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

We obtain the asymptotics for the speed of a particular case of a particle system with branching and selection introduced by Bérard and Gouéré [Comm. Math. Phys.298 (2010) 323–342]. The proof is based on a connection with a supercritical Galton–Watson process censored at a certain level.

A central limit theorem for two-dimensional random walks in a cone

Rodolphe Garbit (2011)

Bulletin de la Société Mathématique de France

We prove that a planar random walk with bounded increments and mean zero which is conditioned to stay in a cone converges weakly to the corresponding Brownian meander if and only if the tail distribution of the exit time from the cone is regularly varying. This condition is satisfied in many natural examples.

A characterization of harmonic measure and Markov processes whose hitting distributions are preserved by rotations translations and dilatations

Bernt Oksendal, Daniel W. Stroock (1982)

Annales de l'institut Fourier

The exit distribution for open sets of a path-continuous, strong Markov process in R n is characterized as a weak star limit of successive spherical sweepings of measures, starting with the unit point mass. Then this is used to prove that two path-continuous strong Markov processes with identical exit distributions from balls when starting form the center, have identical exit distributions from all opens sets, provided they both exit a.s. from bounded sets. This implies that the only path-continuous,...

A characterization of harmonic measures on laminations by hyperbolic Riemann surfaces

Yuri Bakhtin, Matilde Martánez (2008)

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

denotes a (compact, nonsingular) lamination by hyperbolic Riemann surfaces. We prove that a probability measure on is harmonic if and only if it is the projection of a measure on the unit tangent bundle T 1 of which is invariant under both the geodesic and the horocycle flows.

A class of quasigroups solving a problem of ergodic theory

Jonathan D. H. Smith (2000)

Commentationes Mathematicae Universitatis Carolinae

A pointed quasigroup is said to be semicentral if it is principally isotopic to a group via a permutation on one side and a group automorphism on the other. Convex combinations of permutation matrices given by the one-sided multiplications in a semicentral quasigroup then yield doubly stochastic transition matrices of finite Markov chains in which the entropic behaviour at any time is independent of the initial state.

A class of strong limit theorems for countable nonhomogeneous Markov chains on the generalized gambling system

Kangkang Wang (2009)

Czechoslovak Mathematical Journal

In this paper, we study the limit properties of countable nonhomogeneous Markov chains in the generalized gambling system by means of constructing compatible distributions and martingales. By allowing random selection functions to take values in arbitrary intervals, the concept of random selection is generalized. As corollaries, some strong limit theorems and the asymptotic equipartition property (AEP) theorems for countable nonhomogeneous Markov chains in the generalized gambling system are established....

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