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Feynman-Kac penalisations for Brownian motion

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Penalising Brownian Paths

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1969))

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Abstract

Among the various examples of penalisations of Wiener measure discussed in this Monograph, the ones which are obtained by putting a Feynman-Kac type weight with respect to Wiener measure, up to time t, are undoubtedly quite natural, and such transforms of Wiener measure have a long history.

In this Chapter, we show that the asymptotic behavior of all these penalised measures may be expressed in terms of ≥0, σ-finite measures W x on C(ℝ+ → ℝ+). If Λ x denotes the image of W x by the local application, then this positive, σ-finite measure Λ x on the space C(ℝ → ℝ+) characterizes the asymptotic behaviour, as t → ∞, of the law of the Brownian local times(L y t, y ∈ ℝ). These measures Λ x, x ∈ ℝ, are described in detail.

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Authors and Affiliations

  1. Université Nancy I Institut Elie Cartan, Faculté des Sciences Departement Mathésmatiques , B.P. 239 54506 Vandoeuvre-les-Nancy, CX, France

    Bernard Roynette

  2. Université Paris VI Laboratoire de Probabilités, 175 rue de Chevaleret, 75013, Paris, France

    Marc Yor

Authors
  1. Bernard Roynette
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  2. Marc Yor
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Correspondence to Bernard Roynette .

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Roynette, B., Yor, M. (2009). Feynman-Kac penalisations for Brownian motion. In: Penalising Brownian Paths. Lecture Notes in Mathematics(), vol 1969. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89699-9_3

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