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.
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.
Svetlana Janković (1998)
Zbornik Radova
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Tudor, Ciprian A. (2004)
Journal of Applied Mathematics and Stochastic Analysis
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M. Métivier, J. Pellaumail (1976)
Publications mathématiques et informatique de Rennes
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Dorel Barbu, Gheorghe Bocşan (2002)
Czechoslovak Mathematical Journal
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In the present paper, using a Picard type method of approximation, we investigate the global existence of mild solutions for a class of Ito type stochastic differential equations whose coefficients satisfy conditions more general than the Lipschitz and linear growth ones.
M. Métivier, J. Pellaumail (1977)
Publications mathématiques et informatique de Rennes
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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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Fabio Bagarello (2006)
Banach Center Publications
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Marek T. Malinowski, Ravi P. Agarwal (2017)
Czechoslovak Mathematical Journal
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We analyse multivalued stochastic differential equations driven by semimartingales. Such equations are understood as the corresponding multivalued stochastic integral equations. Under suitable conditions, it is shown that the considered multivalued stochastic differential equation admits at least one solution. Then we prove that the set of all solutions is closed and bounded.
Artstein, Zvi, Wets, Roger J.B. (1995)
Journal of Convex Analysis
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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.
Michał Kisielewicz (2001)
Discussiones Mathematicae Probability and Statistics
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Some special selections theorems for stochastic set-valued integrals with respect to the Lebesgue measure are given.