Search results for " 60F10"

showing 2 items of 2 documents

Analysis of random walks on a hexagonal lattice

2019

We consider a discrete-time random walk on the nodes of an unbounded hexagonal lattice. We determine the probability generating functions, the transition probabilities and the relevant moments. The convergence of the stochastic process to a 2-dimensional Brownian motion is also discussed. Furthermore, we obtain some results on its asymptotic behavior making use of large deviation theory. Finally, we investigate the first-passage-time problem of the random walk through a vertical straight-line. Under suitable symmetry assumptions we are able to determine the first-passage-time probabilities in a closed form, which deserve interest in applied fields.

Random walk01 natural sciences010104 statistics & probabilityModerate deviations0103 physical sciencesFOS: MathematicsHexagonal latticeHexagonal latticeProbability-generating functionStatistical physics0101 mathematics010306 general physicsBrownian motionMathematicsStochastic processApplied MathematicsProbability (math.PR)Random walkSymmetry (physics)Random walk; Hexagonal lattice; Probability generating function; Large deviations; Moderate deviations; First-passage timeSettore MAT/06 - Probabilita' e Statistica MatematicaLarge deviationsProbability generating functionLarge deviations theoryFirst-hitting-time modelMathematics - Probability60J15 60F10 82C41First-passage time
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MODERATE DEVIATION PRINCIPLES FOR BIFURCATING MARKOV CHAINS: CASE OF FUNCTIONS DEPENDENT OF ONE VARIABLE

2021

The main purpose of this article is to establish moderate deviation principles for additive functionals of bifurcating Markov chains. Bifurcating Markov chains are a class of processes which are indexed by a regular binary tree. They can be seen as the models which represent the evolution of a trait along a population where each individual has two offsprings. Unlike the previous results of Bitseki, Djellout \& Guillin (2014), we consider here the case of functions which depend only on one variable. So, mainly inspired by the recent works of Bitseki \& Delmas (2020) about the central limit theorem for general additive functionals of bifurcating Markov chains, we give here a moderate deviatio…

Statistics and Probability[MATH.MATH-PR]Mathematics [math]/Probability [math.PR][MATH.MATH-PR] Mathematics [math]/Probability [math.PR]60J80Bifurcating Markov chainsbinary trees[MATH]Mathematics [math]binary trees Mathematics Subject Classification (2020): 60F10deviation inequalitiesMathematics - Probabilitymoderate deviation principles
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