On the convergence of superpositions of a sequence of operators
M. Reichaw (1965)
Studia Mathematica
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M. Reichaw (1965)
Studia Mathematica
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Maslowski, B.
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Aleksander Janicki, Zbigniew Michna, Aleksander Weron (1997)
Applicationes Mathematicae
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In this paper we present a result on convergence of approximate solutions of stochastic differential equations involving integrals with respect to α-stable Lévy motion. We prove an appropriate weak limit theorem, which does not follow from known results on stability properties of stochastic differential equations driven by semimartingales. It assures convergence in law in the Skorokhod topology of sequences of approximate solutions and justifies discrete time schemes applied in computer...
Bohdan Maslowski (1986)
Časopis pro pěstování matematiky
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Aleksander Janicki (1999)
Applicationes Mathematicae
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We present a method of numerical approximation for stochastic integrals involving α-stable Lévy motion as an integrator. Constructions of approximate sums are based on the Poissonian series representation of such random measures. The main result gives an estimate of the rate of convergence of finite-dimensional distributions of finite sums approximating such stochastic integrals. Stochastic integrals driven by such measures are of interest in constructions of models for various problems...
Enrico Priola (2015)
Banach Center Publications
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We consider non-degenerate SDEs with a β-Hölder continuous and bounded drift term and driven by a Lévy noise L which is of α-stable type. If β > 1 - α/2 and α ∈ [1,2), we show pathwise uniqueness and existence of a stochastic flow. We follow the approach of [Priola, Osaka J. Math. 2012] improving the assumptions on the noise L. In our previous paper L was assumed to be non-degenerate, α-stable and symmetric. Here we can also recover relativistic and truncated stable processes and...
Benjelloun, K., Boukas, E.K. (1997)
Mathematical Problems in Engineering
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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.
Adrian Constantin (1994)
Publicacions Matemàtiques
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In this paper we use the Schauder fixed point theorem and methods of integral inequalities in order to prove a result on the existence, uniqueness and parametric dependence on the coefficients of the solution processes in McShane stochastic integral equations.