Abstract
Stoll's construction [7] of Lévy Brownian motion l on ℝd as a white noise integral is used to obtain an action functional I(x) defined for the ‘surfaces’ x of l. This provides a ‘Cameron-Martin’ formula for translation of Lévy measure λ, and also a large deviation principle for scaled Lévy measures λδ. Proofs follow the lines of [2], where nonstandard techniques were used to give natural proofs of the corresponding results for Wiener measure.
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The research for this paper was supported partly by a grant from the SERC.
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Cutland, N.J. An action functional for Lévy Brownian motion. Acta Appl Math 18, 261–281 (1990). https://doi.org/10.1007/BF00049129
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DOI: https://doi.org/10.1007/BF00049129