White noise based stochastic calculus associated with a class of Gaussian processes [PDF]
Opuscula Mathematica, 2012 Using the white noise space setting, we define and study stochastic integrals with respect to a class of stationary increment Gaussian processes. We focus mainly on continuous functions with values in the Kondratiev space of stochastic distributions ...
Daniel Alpay, Haim Attia, David Levanony
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A Numerical Scheme for Harmonic Stochastic Oscillators Based on Asymptotic Expansions
Mathematics, 2022 In this work, we provide a numerical method for discretizing linear stochastic oscillators with high constant frequencies driven by a nonlinear time-varying force and a random force.
Carmela Scalone
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On generalized stochastic fractional integrals and related inequalities
Modern Stochastics: Theory and Applications, 2018 The generalized mean-square fractional integrals ${\mathcal{J}_{\rho ,\lambda ,u+;\omega }^{\sigma }}$ and ${\mathcal{J}_{\rho ,\lambda ,v-;\omega }^{\sigma }}$ of the stochastic process X are introduced.
Hüseyin Budak, Mehmet Zeki Sarikaya
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Aumann Type Set-valued Lebesgue Integral and Representation Theorem [PDF]
International Journal of Computational Intelligence Systems, 2009 n this paper, we shall firstly illustrate why we should discuss the Aumann type set-valued Lebesgue integral of a set-valued stochastic process with respect to time t under the condition that the set-valued stochastic process takes nonempty compact ...
Jungang Li, Shoumei Li
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On approximation of stochastic integrals with respect to a fractional Brownian motion
Lietuvos Matematikos Rinkinys, 2005 There is not abstract.
Kęstutis Kubilius
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Fractional variational problems and particle in cell gyrokinetic simulations with fuzzy logic approach for tokamaks [PDF]
Nuclear Technology and Radiation Protection, 2009 In earlier Rastovic's papers [1] and [2], the effort was given to analyze the stochastic control of tokamaks. In this paper, the deterministic control of tokamak turbulence is investigated via fractional variational calculus, particle in cell simulations,
Rastović Danilo
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Iterated stochastic integrals and random velocity fluctuations
International Journal of Mathematics for Industry, 2023 Iterated stochastic integrals of nonrandom integrands are constructed in the two-dimensional case. They are applied to the velocity fluctuations in a two-dimensional flow and mean kinetic energy of the velocity fluctuations is discussed.
Kouji Yamamuro
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The non-Markovian stochastic Schrodinger equation for open systems [PDF]
, 1997 We present the non-Markovian generalization of the widely used stochastic Schrodinger equation. Our result allows to describe open quantum systems in terms of stochastic state vectors rather than density operators, without approximation.
Caldeira +21 more
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On extended stochastic integrals with respect to Lévy processes
Karpatsʹkì Matematičnì Publìkacìï, 2013 Let $L$ be a Levy process on $[0,+\infty)$. In particular cases, when $L$ is a Wiener or Poisson process, any square integrable random variable can be decomposed in a series of repeated stochastic integrals from nonrandom functions with respect to $L ...
N.A. Kachanovsky
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The Implementation of Milstein Scheme in Two-Dimensional SDEs Using the Fourier Method
Abstract and Applied Analysis, 2018 Multiple stochastic integrals of higher multiplicity cannot always be expressed in terms of simpler stochastic integrals, especially when the Wiener process is multidimensional. In this paper we describe how the Fourier series expansion of Wiener process
Yousef Alnafisah
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