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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A. Plucińska (1971)
Applicationes Mathematicae
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Nadzeya V. Bedziuk, Aleh L. Yablonski (2010)
Banach Center Publications
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We consider an ordinary or stochastic nonlinear equation with generalized coefficients as an equation in differentials in the algebra of new generalized functions in the sense of [8]. Consequently, the solution of such an equation is a new generalized function. We formulate conditions under which the solution of a given equation in the algebra of new generalized functions is associated with an ordinary function or process. Moreover the class of all possible associated functions and processes...
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.
Antoni L. Dawidowicz, Krystyna Twardowska (1988)
Rendiconti del Seminario Matematico della Università di Padova
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Z. Ivković, Yu. A. Rozanov (1972)
Publications de l'Institut Mathématique
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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.
Z. A. Ivković (1969)
Matematički Vesnik
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Adam Paszkiewicz, Jakub Olejnik (2010)
Banach Center Publications
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We describe a new model of multiple reinsurance. The main idea is that the reinsurance premium is paid conditionally. It is motivated by some analysis of the ultimate price of the reinsurance contract. For simplicity we assume that the underlying risk pricing functional is the L₂-norm. An unexpected relation to the general theory of sample regularity of stochastic processes is given.
Peter Jaeger (2016)
Formalized Mathematics
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First we give an implementation in Mizar [2] basic important definitions of stochastic finance, i.e. filtration ([9], pp. 183 and 185), adapted stochastic process ([9], p. 185) and predictable stochastic process ([6], p. 224). Second we give some concrete formalization and verification to real world examples. In article [8] we started to define random variables for a similar presentation to the book [6]. Here we continue this study. Next we define the stochastic process. For further...
Michael Weba (1986)
Mathematische Zeitschrift
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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.
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...
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.
Modeste N’zi, M’hamed Eddahbi (1997)
Applicationes Mathematicae
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By using large deviation techniques, we prove a Strassen type law of the iterated logarithm, in Hölder norm, for Lévy's area process.
Nicolas Privault (1998)
Banach Center Publications
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The aim of this paper is the study of a non-commutative decomposition of the conservation process in quantum stochastic calculus. The probabilistic interpretation of this decomposition uses time changes, in contrast to the spatial shifts used in the interpretation of the creation and annihilation operators on Fock space.