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A functional modulus of continuity for a Wiener process

✍ Scribed by Bin Chen; Miklós Csörgő

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
96 KB
Volume
51
Category
Article
ISSN
0167-7152

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✦ Synopsis

In this paper, we ÿrst establish a large deviation for increments of a Wiener process. A functional modulus of continuity for a Wiener process is presented and proved using this large deviation.

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Let f (x) be a periodic function with period T . In Rivlin (1969) [1] it is claimed that the modulus of continuity is independent of a on [a, a + T ]. In this note we show that this is not correct.