Malliavin calculus for two-parameter processes
D. Nualart, M. Sanz (1985)
Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications
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D. Nualart, M. Sanz (1985)
Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications
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Jean Bertoin (2008)
Journal of the European Mathematical Society
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It was shown in [2] that a Langevin process can be reflected at an energy absorbing boundary. Here, we establish that the law of this reflecting process can be characterized as the unique weak solution to a certain second order stochastic differential equation with constraints, which is in sharp contrast with a deterministic analog.
Zenghu Li, Leonid Mytnik (2011)
Annales de l'I.H.P. Probabilités et statistiques
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General stochastic equations with jumps are studied. We provide criteria for the uniqueness and existence of strong solutions under non-Lipschitz conditions of Yamada–Watanabe type. The results are applied to stochastic equations driven by spectrally positive Lévy processes.
A. Plucińska (1971)
Applicationes Mathematicae
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Michał Kisielewicz (2006)
Discussiones Mathematicae Probability and Statistics
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Some sufficient conditins for tightness of continuous stochastic processes is given. It is verified that in the classical tightness sufficient conditions for continuous stochastic processes it is possible to take a continuous nondecreasing stochastic process instead of a deterministic function one.
Borodin, A.N. (2005)
Zapiski Nauchnykh Seminarov POMI
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Z. Ivković, J. Vukmirović (1976)
Matematički Vesnik
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Aleksander Janicki, Zbigniew Michna, Aleksander Weron (1997)
Applicationes Mathematicae
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In this paper we present a result on convergence of approximate solutions of stochastic differential equations involving integrals with respect to α-stable Lévy motion. We prove an appropriate weak limit theorem, which does not follow from known results on stability properties of stochastic differential equations driven by semimartingales. It assures convergence in law in the Skorokhod topology of sequences of approximate solutions and justifies discrete time schemes applied in computer...
Nicolas Privault (1998)
Banach Center Publications
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The aim of this paper is the study of a non-commutative decomposition of the conservation process in quantum stochastic calculus. The probabilistic interpretation of this decomposition uses time changes, in contrast to the spatial shifts used in the interpretation of the creation and annihilation operators on Fock space.