Rates of convergence to the local time of a diffusion
Jean Jacod (1998)
Annales de l'I.H.P. Probabilités et statistiques
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Jean Jacod (1998)
Annales de l'I.H.P. Probabilités et statistiques
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Gonzalo Perera, Mario Wschebor (2002)
Annales de l'I.H.P. Probabilités et statistiques
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Paavo Salminen, Pierre Vallois (2007)
Annales de l'I.H.P. Probabilités et statistiques
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B. Roynette, P. Vallois, M. Yor (2009)
Annales de l'I.H.P. Probabilités et statistiques
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Limiting laws, as →∞, for brownian motion penalised by the longest length of excursions up to , or up to the last zero before , or again, up to the first zero after , are shown to exist, and are characterized.
Bogdan Iftimie, Étienne Pardoux, Andrey Piatnitski (2008)
Annales de l'I.H.P. Probabilités et statistiques
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This paper deals with the homogenization problem for a one-dimensional parabolic PDE with random stationary mixing coefficients in the presence of a large zero order term. We show that under a proper choice of the scaling factor for the said zero order terms, the family of solutions of the studied problem converges in law, and describe the limit process. It should be noted that the limit dynamics remain random.