Prospective Kolmogorov equation of non-Markovian stochastic processes
A. Plucińska (1971)
Applicationes Mathematicae
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A. Plucińska (1971)
Applicationes Mathematicae
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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.
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...
Z. Ivković, J. Vukmirović (1976)
Matematički Vesnik
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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.
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.
Z. A. Ivković (1969)
Matematički Vesnik
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Jean Bertoin (2008)
Journal of the European Mathematical Society
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It was shown in [2] that a Langevin process can be reflected at an energy absorbing boundary. Here, we establish that the law of this reflecting process can be characterized as the unique weak solution to a certain second order stochastic differential equation with constraints, which is in sharp contrast with a deterministic analog.
M. Métivier, J. Pellaumail (1976)
Publications mathématiques et informatique de Rennes
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J. Gani (1966-1967)
Publications mathématiques et informatique de Rennes
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Fabio Bagarello (2006)
Banach Center Publications
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Sridharan, V., Kalyani, T.V. (2005)
APPS. Applied Sciences
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M. Métivier, J. Pellaumail (1977)
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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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.