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.
M. Métivier, J. Pellaumail (1977)
Publications mathématiques et informatique de Rennes
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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.
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.
M. Métivier, J. Pellaumail (1976)
Publications mathématiques et informatique de Rennes
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Artstein, Zvi, Wets, Roger J.B. (1995)
Journal of Convex Analysis
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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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Witold Bednorz (2008)
Bulletin of the Polish Academy of Sciences. Mathematics
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We show that the main result of [1] on sufficiency of existence of a majorizing measure for boundedness of a stochastic process can be naturally split in two theorems, each of independent interest. The first is that the existence of a majorizing measure is sufficient for the existence of a sequence of admissible nets (as recently introduced by Talagrand [5]), and the second that the existence of a sequence of admissible nets is sufficient for sample boundedness of a stochastic process...
Borisenko, O.V., Borisenko, A.D., Malyshev, I.G. (1994)
Journal of Applied Mathematics and Stochastic Analysis
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K. Florek, E. Marczewski, C. Ryll-Nardzewski (1953)
Studia Mathematica
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Dražen Pantić (1994)
Publications de l'Institut Mathématique
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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.
Akash Sharma, Chanchal Kundu (2024)
Applications of Mathematics
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To have accuracy in the extracted information is the goal of the reliability theory investigation. In information theory, varentropy has recently been proposed to describe and measure the degree of information dispersion around entropy. Theoretical investigation on varentropy of past life has been initiated, however details on its stochastic properties are yet to be discovered. In this paper, we propose a novel stochastic order and introduce new classes of life distributions based on...
Vadym Radchenko (2009)
Studia Mathematica
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The stochastic heat equation on [0,T]×ℝ driven by a general stochastic measure is investigated. Existence and uniqueness of the solution is established. Hölder regularity of the solution in time and space variables is proved.