A sharp upper bound for the expected occupation density of Itô processes with bounded irregular drift and diffusion coefficients

2023/10/19 by Paul Krühner, Shijie Xu, Krühner, Paul +1
Economics, Econometrics and Finance · Mathematics · #60G44 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Statistical Methods and Inference #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2310.12655

openalex publication_date 2023/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

Abstract

We find explicit and optimal upper bounds for the expected occupation density for an Itô-process when its drift and diffusion coefficients are unknown under boundedness and ellipticity conditions on the coefficients. This is related to the optimal bound for the expected interval occupation found in Ankirchner and Wendt(2021). In contrast, our bound is for a single point and the resulting formula is less involved. Our findings allow us to find explicit upper bounds for mean path integrals.

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