Integration by parts formulae for Wiener measures restricted to subsets in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mi mathvariant="double-struck">R</mml:mi><mml:mi>d</mml:mi></mml:msup></mml:math>

Hariya, Yuu

doi:10.1016/j.jfa.2006.06.011

Journal of Functional Analysis

2006

DOI: 10.1016/j.jfa.2006.06.011

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Integration by parts formulae for Wiener measures restricted to subsets in Rd

Yuu Hariya¹

Abstract: We study an integration by parts formula for a pinned Wiener measure restricted to a space of paths staying within a subset in R d . The result presented here generalizes the formula in [L. Zambotti, Integration by parts formulae on convex sets of paths and applications to SPDEs with reflection, Probab. Theory Relat. Fields 123 (2002) 579-600] for the case of a half-line in R.

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Cited by 9 publications

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Integration by parts on the law of the modulus of the Brownian bridge

Grothaus

Voßhall

2018

Stoch PDE: Anal Comp

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We prove an infinite dimensional integration by parts formula on the law of the modulus of the Brownian bridge BB = (BB t ) 0≤t≤1 from 0 to 0 in use of methods from white noise analysis and Dirichlet form theory. Additionally to the usual drift term, this formula contains a distribution which is constructed in the space of Hida distributions by means of a Wick product with Donsker's delta (which correlates with the local time of |BB| at zero). This additional distribution corresponds to the reflection at zero caused by the modulus.Mathematics Subject Classification 2010: 60H07, 60H40, 46F25, 31C25 Keywords: reflected Brownian bridge, integration by parts formula in infinite dimensions, stochastic heat equation with reflection, white noise analysis, Dirichlet forms t for a pathwise regularization (B ε,t ) t≥0 of the Brownian motion and (:Ḃ 2 ε,t :) t≥0 the renormalization of the square of its derivative (similar to the definitions for the case of the Brownian bridge given

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Integration by parts on the law of the modulus of the Brownian bridge

Grothaus

Voßhall

2018

Stoch PDE: Anal Comp

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Cameron–Martin formula for the σ-finite measure unifying Brownian penalisations

Yano¹

2010

Journal of Functional Analysis

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Quasi-invariance under translation is established for the σ -finite measure unifying Brownian penalisations, which has been introduced by Najnudel, Roynette and Yor [J. Najnudel, B. Roynette, M. Yor, A remarkable σ -finite measure on C(R + , R) related to many Brownian penalisations, C. R. Math. Acad. Sci. Paris 345 (8) (2007) 459-466]. For this purpose, the theory of Wiener integrals for centered Bessel processes, due to Funaki, Hariya and Yor [T. Funaki, Y. Hariya, M. Yor, Wiener integrals for centered Bessel and related processes. II, ALEA Lat. Am. J. Probab. Math. Stat. 1 (2006) 225-240 (electronic)], plays a key role.

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Poincaré inequality for linear SPDE driven by Lévy Noise

Xie

2010

Stochastic Processes and their Applications

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Integration by parts formulae for Wiener measures restricted to subsets in Rd

Cited by 9 publications

References 10 publications

Integration by parts on the law of the modulus of the Brownian bridge

Integration by parts on the law of the modulus of the Brownian bridge

Cameron–Martin formula for the σ-finite measure unifying Brownian penalisations

Poincaré inequality for linear SPDE driven by Lévy Noise

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