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• W2046674598 abstract "We consider the law ν of the Bessel Bridge of dimension 3 on the convex set K 0 of continuous non-negative paths on [0,1]. We prove an integration by parts formula on K 0 w.r.t. to ν, where an explicit infinite-dimensional boundary measure σ appears. We apply this to the solution (u,η) of a white-noise driven stochastic partial differential equation with reflection introduced by Nualart and Pardoux, where u:[0, ∞) ×[0,1] ↦ℝ+ is a random non-negative function and η is a random positive measure on [0, ∞) × (0,1). Indeed, we prove that u is the radial part in the sense of Dirichlet Forms of the ℝ3-valued solution of a linear stochastic heat equation, and that η has the following structure: s ↦ 2η([0,s],(0,1)) is the Additive Functional of u with Revuz measure σ for η(ds,(0,1))-a.e. s, there exists a unique r(s)in(0,1) s.t. u(s,r(s))=0, and η(ds,dθ)=δ r(s) (dθ)η(ds,(0,1)), where δ a is the Dirac mass at a ?(0,1). This gives a complete description of (u, η) as solution of a Skorohod Problem in the infinite-dimensional non-smooth convex set K 0 ." @default.
• W2046674598 created "2016-06-24" @default.
• W2046674598 creator A5027690861 @default.
• W2046674598 date "2002-08-01" @default.
• W2046674598 modified "2023-10-16" @default.
• W2046674598 title "Integration by parts formulae on convex sets of paths and applications to SPDEs with reflection" @default.
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• W2046674598 doi "https://doi.org/10.1007/s004400200203" @default.
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