Displaying similar documents to “Computer-aided modeling and simulation of electrical circuits with α-stable noise”

Computer simulation of a nonlinear model for electrical circuits with α-stable noise

Aleksander Janicki (1995)

Applicationes Mathematicae

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The aim of this paper is to apply the appropriate numerical, statistical and computer techniques to the construction of approximate solutions to nonlinear 2nd order stochastic differential equations modeling some engineering systems subject to large random external disturbances. This provides us with quantitative results on their asymptotic behavior.

Stochastic flow for SDEs with jumps and irregular drift term

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...

Approximation of stochastic differential equations driven by α-stable Lévy motion

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...

Approximation of finite-dimensional distributions for integrals driven by α-stable Lévy motion

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...

Exponential ergodicity of semilinear equations driven by Lévy processes in Hilbert spaces

Anna Chojnowska-Michalik, Beniamin Goldys (2015)

Banach Center Publications

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We study convergence to the invariant measure for a class of semilinear stochastic evolution equations driven by Lévy noise, including the case of cylindrical noise. For a certain class of equations we prove the exponential rate of convergence in the norm of total variation. Our general result is applied to a number of specific equations driven by cylindrical symmetric α-stable noise and/or cylindrical Wiener noise. We also consider the case of a "singular" Wiener process with unbounded...

Fractional Fokker-Planck-Kolmogorov type Equations and their Associated Stochastic Differential Equations

Hahn, Marjorie, Umarov, Sabir (2011)

Fractional Calculus and Applied Analysis

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MSC 2010: 26A33, 35R11, 35R60, 35Q84, 60H10 Dedicated to 80-th anniversary of Professor Rudolf Gorenflo There is a well-known relationship between the Itô stochastic differential equations (SDEs) and the associated partial differential equations called Fokker-Planck equations, also called Kolmogorov equations. The Brownian motion plays the role of the basic driving process for SDEs. This paper provides fractional generalizations of the triple relationship between the driving...