Cauchy's principal value of local times of Lévy processes with no negative jumps via continuous branching processes.
Bertoin, Jean (1997)
Electronic Journal of Probability [electronic only]
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Bertoin, Jean (1997)
Electronic Journal of Probability [electronic only]
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Wang, Hao (2002)
Electronic Communications in Probability [electronic only]
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Birkner, Matthias, Blath, Jochen, Capaldo, Marcella, Etheridge, Alison M., Möhle, Martin, Schweinsberg, Jason, Wakolbinger, Anton (2005)
Electronic Journal of Probability [electronic only]
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Champagnat, Nicolas, Roelly, Sylvie (2008)
Electronic Journal of Probability [electronic only]
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Pierre Étoré, Antoine Lejay (2007)
ESAIM: Probability and Statistics
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In this paper, we prove a Donsker theorem for one-dimensional processes generated by an operator with measurable coefficients. We construct a random walk on any grid on the state space, using the transition probabilities of the approximated process, and the conditional average times it spends on each cell of the grid. Indeed we can compute these quantities by solving some suitable elliptic PDE problems.
Dawson, Donald A., Li, Zenghu, Wang, Hao (2001)
Electronic Journal of Probability [electronic only]
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Dawson, D.A., Gorostiza, L.G., Wakolbinger, A. (2004)
Electronic Journal of Probability [electronic only]
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Li, Zenghu, Shiga, Tokuzo, Yao, Lihua (1999)
Electronic Communications in Probability [electronic only]
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Luschgy, Harald, Pagès, Gilles (2008)
Electronic Communications in Probability [electronic only]
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Benjamin Jourdain, Tony Lelièvre, Raphaël Roux (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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We study a free energy computation procedure, introduced in [Darve and Pohorille, (2001) 9169–9183; Hénin and Chipot, (2004) 2904–2914], which relies on the long-time behavior of a nonlinear stochastic differential equation. This nonlinearity comes from a conditional expectation computed with respect to one coordinate of the solution. The long-time convergence of the solutions to this equation has been proved in [Lelièvre , (2008)...