A generalized Itô-Ventzell formula. Application to a class of anticipating stochastic differential equations
Daniel Ocone, Etienne Pardoux (1989)
Annales de l'I.H.P. Probabilités et statistiques
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Daniel Ocone, Etienne Pardoux (1989)
Annales de l'I.H.P. Probabilités et statistiques
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T. Barth, A. U. Kussmaul (1981)
Annales scientifiques de l'Université de Clermont. Mathématiques
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J. Campos, F. Plo, M. San Miguel (1993)
Revista Matemática de la Universidad Complutense de Madrid
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Stochastic Petri nets generalize the notion of queuing systems and are a useful model in performance evaluation of parallel and distributed systems. We give necessary and sufficient conditions for the boundedness of a stochastic process related to these nets.
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...
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.
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.
Vigirdas Mackevičius (1987)
Annales de l'I.H.P. Probabilités et statistiques
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Peter Jaeger (2017)
Formalized Mathematics
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We start with the definition of stopping time according to [4], p.283. We prove, that different definitions for stopping time can coincide. We give examples of stopping time using constant-functions or functions defined with the operator max or min (defined in [6], pp.37–38). Finally we give an example with some given filtration. Stopping time is very important for stochastic finance. A stopping time is the moment, where a certain event occurs ([7], p.372) and can be used together with...
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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