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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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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DOI: https://doi.org/10.1007/978-3-540-89699-9_3
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