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• W3139969500 abstract "Let $B={ B_{t}} _{tge 0}$ be a one-dimensional standard Brownian motion and denote by $A_{t},,tge 0$, the quadratic variation of the geometric Brownian motion $e^{B_{t}},,tge 0$. Bougerol's celebrated identity (1983) asserts that, if $beta ={ beta (t)} _{tge 0}$ is another Brownian motion independent of $B$, then $beta (A_{t})$ is identical in law with $sinh B_{t}$ for every fixed $t>0$. In this paper, we extend Bougerol's identity to an identity in law for processes up to time $t$, which exhibits a certain invariance of the law of Brownian motion. The extension is described in terms of anticipative transforms of $B$ involving $A_{t}$ as an anticipating factor. A Girsanov-type formula for those transforms is shown. An extension of a variant of Bougerol's identity is also presented." @default.
• W3139969500 created "2021-04-13" @default.
• W3139969500 creator A5075382898 @default.
• W3139969500 date "2021-04-05" @default.
• W3139969500 modified "2023-09-27" @default.
• W3139969500 title "Extensions of Bougerol's identity in law and the associated anticipative path transformations" @default.
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• W3139969500 hasPublicationYear "2021" @default.
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