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The aim of this paper is to find a formula for the double Laplace transform of the truncated variation of a Brownian motion with drift. In order to find the double Laplace transform, we also prove some identities for the Brownian motion with drift, which may be of independent interest.
The main objective of this paper is to establish a large deviation principle for heat kernel measures on loop spaces. It gives an extension of Fang and Zhang's results on loop groups. For the proof, we use the continuity theorem of Lyons' rough path theory.
The metric entropy of absolute convex hulls of sets in Hilbert spaces is studied for the general case when the metric entropy of the sets is arbitrary. Under some regularity assumptions, the results are sharp.
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