Fluctuations of bridges, reciprocal characteristics, and concentration\n of measure

2016/02/23 by Giovanni Conforti, Conforti, Giovanni · 1 citation
Mathematics · #Stochastic processes and statistical mechanics #Mathematical Dynamics and Fractals #Markov Chains and Monte Carlo Methods

paper · pdf · doi:10.48550/arxiv.1602.07231

Abstract

Conditions on the generator of a Markov process to control the fluctuations\nof its bridges are found. In particular, continuous time random walks on graphs\nand gradient diffusions are considered. Under these conditions, a concentration\nof measure inequality for the marginals of the bridge of a gradient diffusion\nand refined large deviation expansions for the tails of a random walk on a\ngraph are derived. In contrast with the existing literature about bridges, all\nthe estimates we obtain hold for non asymptotic time scales. New concentration\nof measure inequalities for pinned Poisson random vectors are also established.\nThe quantities expressing our conditions are the so called \reciprocal\ncharacteristics associated with the Markov generator.\n

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