On the existence and regularity of local times

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Date

2024-07-30

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Department of Information and Service Management

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Mcode

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Language

en

Pages

27

Series

Electronic Journal of Probability, Volume 29

Abstract

We study the existence and regularity of local times for general d-dimensional stochastic processes. We give a general condition for their existence and regularity properties. To emphasize the contribution of our results, we show that they include various prominent examples, among others solutions to stochastic differential equations driven by fractional Brownian motion, where the behavior of the local time was not fully understood up to now and remained as an open problem in the stochastic analysis literature. In particular this completes the picture regarding the local time behavior of such equations, above all includes all possible dimensions and Hurst parameters. As other main examples, we also show that by using our general approach, one can quite easily cover and extend some recently obtained results on the local times of the Rosenblatt process and Gaussian quasi-helices.

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Publisher Copyright: © 2024, Institute of Mathematical Statistics. All rights reserved.

Keywords

fractional Brownian motion, Gaussian quasi-helices, local time, Malliavin calculus, regularity, Rosenblatt process, stochastic differential equations

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DOI

10.1214/24-EJP1172

Citation

Sottinen, T, Sönmez, E & Viitasaari, L 2024, ' On the existence and regularity of local times ', Electronic Journal of Probability, vol. 29, 107 . https://doi.org/10.1214/24-EJP1172

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https://urn.fi/URN:NBN:fi:aalto-202504023058

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