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A non-linear Riesz respresentation in probabilistic potential theory [PDF]
Annales de l'Institut Henri Poincare (B) Probability and Statistics, 2005 Let \((X_t)_{t\geq 0}\) be a Hunt process on a locally compact metric space \(S\). Define the nonlinear potential operator \(\overline{G}\) by \(\overline{G}f(x)=E_x\left(\int_0^\zeta \sup_{0\leq s\leq t} f(X_s) dt\right)\). The main purpose of this paper is to show the Riesz decomposition theorem relative to this potential, that is, for a given ...
Nicole El-Karoui, Hans Föllmer
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Probabilistic potential theory and induction of dynamical systems [PDF]
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 2021 In this article, we outline a version of a balayage formula in probabilistic potential theory adapted to measure-preserving dynamical systems. This balayage identity generalizes the property that induced maps preserve the restriction of the original invariant measure. As an application, we prove in some cases the invariance under induction of the Green-
Françoise Pène, Damien Thomine
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Solving Semilinear Partial Differential Equations With Probabilistic Potential Theory [PDF]
Transactions of the American Mathematical Society, 1985 Techniques of probabilistic potential theory are applied to solve − L u + f ( u ) = μ - Lu + f(u) = \mu , where μ \mu is a signed measure, f f a (possibly discontinuous) function and L L a second order elliptic or ...
Joseph Glover, P. J. McKenna
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J. L. Doob: Foundations of stochastic processes and probabilistic potential theory [PDF]
The Annals of Probability, 2009 Published in at http://dx.doi.org/10.1214/09-AOP465 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Ronald Getoor
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How to clean a dirty floor: Probabilistic potential theory and the Dobrushin uniqueness theorem [PDF]
Markov Processes and Related Fields, 2007 Motivated by the Dobrushin uniqueness theorem in statistical mechanics, we consider the following situation: Let be a nonnegative matrix over a finite or countably infinite index set X, and define the "cleaning operators" _h = I_{1-h} + I_h for h: X \to [0,1] (here I_f denotes the diagonal matrix with entries f).
Thierry de la Rue +2 more
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PROBABILISTIC APPROACH IN POTENTIAL THEORY TO THE EQUILIBRIUM PROBLEM [PDF]
Annales de l'Institut Fourier, 2008 A complete form of the classical theorem by Gauss-M. Riesz-Frostman is given for a large of Markov processes without the usual hypothesis of duality. The idea leads to a probabilistic solution of Robin’s problem and it is based on the last exit time from a transient set.
Kai Lai Chung
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How to make unforgeable money in generalised probabilistic theories [PDF]
Quantum, 2018 We discuss the possibility of creating money that is physically impossible to counterfeit. Of course, "physically impossible" is dependent on the theory that is a faithful description of nature.
John H. Selby, Jamie Sikora
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Some analytic aspects of probabilistic potential theory [PDF]
Applicationes Mathematicae, 1969 Z. Ciesielski, M. Kac
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Duke Mathematical Journal, 1993 We study the existence of solutions to the problem \[ \begin{cases} \Delta u+K(x) f(u)=0 \quad & \text{ in } D \\ u>0 & \text{ in } D \\ u=0 & \text{ on } \partial D. \end{cases} \tag{I} \] Our goal is to prove an existence theorem for problem (I) in a general setting by using Brownian path integration method and the potential theory.
Zhengyang Zhao
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Book Review: Classical potential theory and its probabilistic counterpart [PDF]
Bulletin of the American Mathematical Society, 1985 P. A. Meyer
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