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AIP Advances, 2023 Stochastic methods significantly solve stochastic differential equations such as stochastic equations with a delay, stochastic fractional and fractal equations, stochastic partial differential equations, and many more.
Wafa F. Alfwzan +5 more
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Equations Related to Stochastic Processes: Semigroup Approach and Fourier Transform
Современная математика: Фундаментальные направления, 2021 The work is devoted to integro-differential equations related to stochastic processes. We study the relationship between differential equations with random perturbations - stochastic differential equations (SDEs) - and deterministic equations for the ...
I. V. Melnikova +2 more
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Harmonic analysis of stochastic equations and backward stochastic differential equations [PDF]
Probability Theory and Related Fields, 2008 The BMO martingale theory is extensively used to study nonlinear multi-dimensional stochastic equations (SEs) in $\cR^p$ ($p\in [1, \infty)$) and backward stochastic differential equations (BSDEs) in $\cR^p\times \cH^p$ ($p\in (1, \infty)$) and in $\cR^\infty\times \bar{\cH^\infty}^{BMO}$, with the coefficients being allowed to be unbounded.
Delbaen, Freddy, Tang, Shanjian
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Stochastic Gauss equations [PDF]
Celestial Mechanics and Dynamical Astronomy, 2015 We derive the equations of celestial mechanics governing the variations of the orbital elements under a stochastic perturbation generalizing the classical Gauss equations. Explicit formulas are given for the semi-major axis, the eccentricity, the inclination, the longitude of the ascending node, the pericenter angle and the mean anomaly which are ...
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STOCHASTIC EINSTEIN EQUATIONS [PDF]
International Journal of Geometric Methods in Modern Physics, 2011 Stochastic Einstein equations are considered when three-dimensional space metric γij are stochastic functions. The probability density for the stochastic quantities is connected with Perelman's entropy functional. As an example, the Friedman Universe is considered. It is shown that for the Friedman Universe the dynamical evolution is not changed.
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Delayed Stochastic Linear-Quadratic Control Problem and Related Applications
Journal of Applied Mathematics, 2012 We discuss a quadratic criterion optimal control problem for stochastic linear system with delay in both state and control variables. This problem will lead to a kind of generalized forward-backward stochastic differential equations (FBSDEs) with Itô’s ...
Li Chen, Zhen Wu, Zhiyong Yu
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Fractional SDEs with stochastic forcing: Existence, uniqueness, and approximation
Nonlinear Analysis, 2023 In this article, we are interested in fractional stochastic differential equations (FSDEs) with stochastic forcing, i.e., to FSDE we add a stochastic forcing term.
Kęstutis Kubilius
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Martingale Decomposition and Backward Stochastic Dynamic Equations on Time Scales
Journal of Mathematics, 2022 The paper aims to establish the related backward stochastic dynamic equations on time scales, BS ∇ Es for short, concerning to ∇-integral on time scales.
Guofeng Tang, Guangyan Jia
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Stochastic Loop Equations [PDF]
International Journal of Modern Physics A, 1997 Stochastic quantization is applied to derivation of the equations for the Wilson loops and generating functionals of the Wilson loops in the N = ∞ limit. These equations are treated both in the coordinate and momentum representations. In the first case the connection of the suggested approach with the problem of random closed contours and ...
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Bisimulation Relations Between Automata, Stochastic Differential Equations and Petri Nets [PDF]
Electronic Proceedings in Theoretical Computer Science, 2010 Two formal stochastic models are said to be bisimilar if their solutions as a stochastic process are probabilistically equivalent. Bisimilarity between two stochastic model formalisms means that the strengths of one stochastic model formalism can be used
Mariken H.C. Everdij, Henk A.P. Blom
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