Displaying similar documents to “Structural properties and limit behaviour of linear stochastic systems in Hilbert spaces”

Stochastic differential equation driven by a pure-birth process

Marta Tyran-Kamińska (2002)

Annales Polonici Mathematici

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A generalization of the Poisson driven stochastic differential equation is considered. A sufficient condition for asymptotic stability of a discrete time-nonhomogeneous Markov process is proved.

Invariant measures for nonlinear SPDE's: uniqueness and stability

Bohdan Maslowski, Jan Seidler (1998)

Archivum Mathematicum

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The paper presents a review of some recent results on uniqueness of invariant measures for stochastic differential equations in infinite-dimensional state spaces, with particular attention paid to stochastic partial differential equations. Related results on asymptotic behaviour of solutions like ergodic theorems and convergence of probability laws of solutions in strong and weak topologies are also reviewed.

Tightness of Continuous Stochastic Processes

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.

An averaging principle for stochastic evolution equations. II.

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.

Equations in differentials in the algebra of generalized stochastic processes

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...

Stochastic differential inclusions

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.