Uniform in time modulus of continuity of Brownian motion
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915402016096256 |
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| author | Chevallier, Julien |
| author_facet | Chevallier, Julien |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_15931 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Uniform in time modulus of continuity of Brownian motion Chevallier, Julien Probability 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. |
| title | Uniform in time modulus of continuity of Brownian motion |
| topic | Probability |
| url | https://arxiv.org/abs/2312.15931 |