Penalizing null recurrent diffusions

2011/11/14 by Christophe Profeta, Profeta, Christophe
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1111.3343

arxiv created 2011/11/14 · openalex publication_date 2011/11/14 · arxiv updated 2011/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present some limit theorems for the normalized laws (with respect to functionals involving last passage times at a given level up to time t) of a large class of null recurrent diffusions. Our results rely on hypotheses on the Lévy measure of the diffusion inverse local time at 0. As a special case, we recover some of the penalization results obtained by Najnudel, Roynette and Yor in the (reflected) Brownian setting.

Citations

• A Theorem on Sums of Independent Positive Random Variables and Its Applications to Branching Random Processes

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