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.
Martin Ondreját
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Different types of uniqueness (e.g. pathwise uniqueness, uniqueness in law, joint uniqueness in law) and existence (e.g. strong solution, martingale solution) for stochastic evolution equations driven by a Wiener process are studied and compared. We show a sufficient condition for a joint distribution of a process and a Wiener process to be a solution of a given SPDE. Equivalences between different concepts of solution are shown. An alternative approach to the construction of the stochastic...
István Gyöngy, Teresa Martínez (2001)
Czechoslovak Mathematical Journal
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We study the regularizing effect of the noise on differential equations with irregular coefficients. We present existence and uniqueness theorems for stochastic differential equations with locally unbounded drift.
Svetlana Janković (1998)
Zbornik Radova
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J. G. Dijkman (1965-1966)
Compositio Mathematica
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Hiroshi Kaneko, Shintaro Nakao (1988)
Séminaire de probabilités de Strasbourg
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Toshio Yamada (1976)
Séminaire de probabilités de Strasbourg
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T. Barth, A. U. Kussmaul (1981)
Annales scientifiques de l'Université de Clermont. Mathématiques
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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.