Relative entropy and stability of stochastic semigroups
Krzysztof Łoskot, Ryszard Rudnicki (1991)
Annales Polonici Mathematici
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Krzysztof Łoskot, Ryszard Rudnicki (1991)
Annales Polonici Mathematici
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Bohdan Maslowski, Jan Seidler, Ivo Vrkoč (1991)
Mathematica Bohemica
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In the present paper integral continuity theorems for solutions of stochastic evolution equations of parabolic type on unbounded time intervals are established. For this purpose, the asymptotic stability of stochastic partial differential equations is investigated, the results obtained being of independent interest. Stochastic evolution equations are treated as equations in Hilbert spaces within the framework of the semigroup approach.
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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Sridharan, V., Kalyani, T.V. (2005)
APPS. Applied Sciences
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Fabio Bagarello (2006)
Banach Center Publications
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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.
Artstein, Zvi, Wets, Roger J.B. (1995)
Journal of Convex Analysis
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M. Métivier, J. Pellaumail (1977)
Publications mathématiques et informatique de Rennes
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Michael C. Mackey, Marta Tyran-Kamińska (2008)
Annales Polonici Mathematici
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A new sufficient condition is proved for the existence of stochastic semigroups generated by the sum of two unbounded operators. It is applied to one-dimensional piecewise deterministic Markov processes, where we also discuss the existence of a unique stationary density and give sufficient conditions for asymptotic stability.
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.
Tuğrul Dayar, Jean-Michel Fourneau, Nihal Pekergin (2010)
RAIRO - Operations Research
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We present a transformation for stochastic matrices and analyze the effects of using it in stochastic comparison with the strong stochastic (st) order. We show that unless the given stochastic matrix is row diagonally dominant, the transformed matrix provides better st bounds on the steady state probability distribution.