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Preprints, Working Papers, ... Year : 2023

Uniform in time modulus of continuity of Brownian motion

Abstract

Let $B=(B_t)_{t\geq 0}$ be a standard Brownian motion. The main objective is to find a uniform (in time) control of the modulus of continuity of $B$ in the spirit of what appears in (Kurtz, 1978). More precisely, it involves the control of the exponential moments of the random variable $\sup_{0\leq s\leq t} |B_t-B_s|/w(t,|t-s|)$ for a suitable function $w$. A stability inequality for diffusion processes is then derived and applied to two simple frameworks.
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hal-04361156 , version 1 (22-12-2023)

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Julien Chevallier. Uniform in time modulus of continuity of Brownian motion. 2023. ⟨hal-04361156⟩
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