The Banach fixed point method for Ito stochastic differential equations
T. Barth, A. U. Kussmaul (1981)
Annales scientifiques de l'Université de Clermont. Mathématiques
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T. Barth, A. U. Kussmaul (1981)
Annales scientifiques de l'Université de Clermont. Mathématiques
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Giuseppe Da Prato (2015)
Banach Center Publications
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We consider a stochastic evolution equation in a separable Hilbert spaces H or in a separable Banach space E with a Hölder continuous perturbation on the drift. We review some recent result about pathwise uniqueness for this equation.
Michał Kisielewicz (1997)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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The definition and some existence theorems for stochastic differential inclusions depending only on selections theorems are given.
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.
Z. Ivković, J. Vukmirović (1976)
Matematički Vesnik
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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.
Micha Kisielewicz (2003)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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The Girsanov's theorem is useful as well in the general theory of stochastic analysis as well in its applications. We show here that it can be also applied to the theory of stochastic differential inclusions. In particular, we obtain some special properties of sets of weak solutions to some type of these inclusions.
M. Métivier, J. Pellaumail (1976)
Publications mathématiques et informatique de Rennes
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Michał Kisielewicz (1999)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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The definition and some existence theorems for stochastic differential inclusion dZₜ ∈ F(Zₜ)dXₜ, where F and X are set valued stochastic processes, are given.
Dražen Pantić (1994)
Publications de l'Institut Mathématique
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A. Plucińska (1971)
Applicationes Mathematicae
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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.
J. Gani (1966-1967)
Publications mathématiques et informatique de Rennes
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Sridharan, V., Kalyani, T.V. (2005)
APPS. Applied Sciences
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