Results 11 to 20 of about 329,029 (283)
Set-Valued Stochastic Lebesque Integral and Representation Theorems [PDF]
International Journal of Computational Intelligence Systems, 2008 In this paper, we shall firstly illustrate why we should introduce set-valued stochastic integrals, and then we shall discuss some properties of set-valued stochastic processes and the relation between a set-valued stochastic process and its selection ...
Jungang Li, Shoumei Li
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On the complexity of stochastic integration [PDF]
Mathematics of Computation, 2000 Fix \(T,L,K>0\), and consider functions \(f\) of \([0,T]\times \mathbb{R}\) into \(\mathbb{R}\) such that \(\partial_1f\) and \(\partial^2_2f\) are continuous, and bounded by \(L,K\), respectively. Set \(I(f):= \int^T_0 f(t,B_t)dB_t\), \(B_t\) being a Brownian motion, and for \(n\in\mathbb{N}^*\): \[ \begin{multlined} A_n(f):= \sum^n_{j=1} f\bigl(((j-1)
Grzegorz W. Wasilkowski +1 more
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Feynman--Kac formula for the heat equation driven by fractional noise with Hurst parameter $H<1/2$ [PDF]
, 2012 In this paper, a Feynman-Kac formula is established for stochastic partial differential equation driven by Gaussian noise which is, with respect to time, a fractional Brownian motion with Hurst parameter ...
Hu, Yaozhong, Lu, Fei, Nualart, David
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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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Karpatsʹkì Matematičnì Publìkacìï, 2022 We deal with spaces of regular test functions in the Lévy white noise analysis, which are constructed using Lytvynov's generalization of a chaotic representation property.
N.A. Kachanovsky
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Gibbs measures with double stochastic integrals on a path space [PDF]
, 2007 We investigate Gibbs measures relative to Brownian motion in the case when the interaction energy is given by a double stochastic integral. In the case when the double stochastic integral is originating from the Pauli-Fierz model in nonrelativistic ...
Betz, Volker, Hiroshima, Fumio
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Directional Stochastic Orders with an Application to Financial Mathematics
Mathematics, 2021 Relevant integral stochastic orders share a common mathematical model, they are defined by generators which are made up of increasing functions on appropriate directions. Motivated by the aim to provide a unified study of those orders, we introduce a new
María Concepción López-Díaz +2 more
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Pathwise solvability of stochastic integral equations with generalized drift and non-smooth dispersion functions [PDF]
, 2016 We study one-dimensional stochastic integral equations with non-smooth dispersion coefficients, and with drift components that are not restricted to be absolutely continuous with respect to Lebesgue measure.
Karatzas, Ioannis, Ruf, Johannes
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Backward stochastic variational inequalities driven by multidimensional fractional Brownian motion [PDF]
Opuscula Mathematica, 2018 We study the existence and uniqueness of the backward stochastic variational inequalities driven by \(m\)-dimensional fractional Brownian motion with Hurst parameters \(H_k\) (\(k=1,\ldots m\)) greater than \(1/2\).
Dariusz Borkowski +1 more
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Set-Valued Stochastic Equation with Set-Valued Square Integrable Martingale
ITM Web of Conferences, 2017 In this paper, we shall introduce the stochastic integral of a stochastic process with respect to set-valued square integrable martingale. Then we shall give the Aumann integral measurable theorem, and give the set-valued stochastic Lebesgue integral and
Li Jun-Gang, Zheng Shi-Qing
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