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Entropy, 2004 We define heat kernel measure on punctured spheres. The random field which is got by this procedure is not Gaussian. We define a stochastic line bundle on the loop space, such that the punctured sphere corresponds to a generalized parallel transport on ...
Rémi Léandre
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Integration with Stochastic Point Processes [PDF]
ACM Transactions on Graphics, 2016 We present a novel comprehensive approach for studying error in integral estimation with point distributions based on point process statistics. We derive exact formulae for bias and variance of integral estimates in terms of the spatial or spectral characteristics of integrands and first- and-second order product density measures of general point ...
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Construction of Lyapunov functions from first integrals for stochastic stability analysis
Applied and Computational MechanicsThis paper explores the application of first integrals in constructing Lyapunov functions for stability analysis of dynamical systems in stochastic domains. A key advantage of using first integrals is their ability to embed system-specific structural and
Náprstek J., Fischer C.
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Karpatsʹkì Matematičnì Publìkacìï, 2022 A new generalization of the Katugampola generalized fractional integrals in terms of the Mittag-Leffler functions is proposed. Consequently, new generalizations of the Hermite-Hadamard inequalities by this newly proposed fractional integral operator, for
M. Omaba
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Chaotic expansion in the G-expectation space [PDF]
Opuscula Mathematica, 2013 In this paper, we are motivated by uncertainty problems in volatility. We prove the equivalent theorem of Wiener chaos with respect to \(G\)-Brownian motion in the framework of a sublinear expectation space.
Hacène Boutabia, Imen Grabsia
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The Range of Stochastic Integration
The Annals of Probability, 1978 Every measurable real-valued function $f$ on the space of Wiener process paths with $E(|f|^p) < \infty$ (where $0 < p < 1$) can be represented as a stochastic integral $f = \int \varphi dX$, where $E(\int \varphi^2(t)dt)^{p/2} < \infty$. A similar result holds for $1 < p < \infty$ if and only if $E(f) = 0$.
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Efficient discretization of stochastic integrals [PDF]
Finance and Stochastics, 2013 Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves seemingly new. Asymptotically efficient schemes which attain the lower bounds are constructed explicitly.
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A Comparison of Stochastic Integrals
The Annals of Probability, 1979 the existence of the star integral, we give a formula relating the two integrals. We show that the star integral is equal to the dot integral provided one takes a projection of the integrand onto the space of predictable processes before evaluating the dot integral.
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Random representation of Blasius’ formula through stochastic complex integrals
International Journal of Mathematics for Industry, 2019 Two-dimensional flow is considered in the complex plane. We discuss Blasius’ formula in a perfect fluid through stochastic complex integrals. This formula is also investigated in a viscous fluid.
Kouji Yamamuro
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Journal of Harbin University of Science and Technology, 2022 The applications of the theories of square-mean almost automorphic type functions have attracted more and more attention by mathematics researchers, square-mean asymptotically almost automorphic solutions of this class of differential equations have a ...
YAO Hui-li +3 more
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