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arXiv · 2112.00401

Stochastic integration with respect to local time of the Brownian sheet and regularising properties of Brownian sheet paths

Antoine-Marie Bogso·Moustapha Dieye·Olivier Menoukeu Pamen
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Abstract

In this work, we generalise the stochastic local time space integration introduced in \cite{Ei00} to the case of Brownian sheet. %We develop a stochastic local time-space calculus with respect to the Brownian sheet. This allows us to prove a generalised two-parameter It\^o formula and derive Davie type inequalities for the Brownian sheet. Such estimates are useful to obtain regularity bounds for some averaging type operators along Brownian sheet curves.

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Antoine-Marie Bogso, Moustapha Dieye, Olivier Menoukeu Pamen. 2021-12-01. Stochastic integration with respect to local time of the Brownian sheet and regularising properties of Brownian sheet paths. https://doi.org/10.3150/22-bej1555

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