Properties of solution set of stochastic inclusions.
Kisielewicz, Michał (1993)
Journal of Applied Mathematics and Stochastic Analysis
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Kisielewicz, Michał (1993)
Journal of Applied Mathematics and Stochastic Analysis
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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.
T. Barth, A. U. Kussmaul (1981)
Annales scientifiques de l'Université de Clermont. Mathématiques
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Michel Métivier (1982)
Séminaire de probabilités de Strasbourg
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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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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.
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.
Z. Ivković, J. Vukmirović (1976)
Matematički Vesnik
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J. M. Angulo Ibáñez, R. Gutiérrez Jáimez (1988)
Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications
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Anna Chojnowska-Michalik (1979)
Banach Center Publications
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Joachim Syga (2015)
Discussiones Mathematicae Probability and Statistics
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A random measure associated to a semimartingale is introduced. We use it to investigate properties of several types of stochastic integrals and properties of the solution set of Stratonovich-type stochastic inclusion.