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An Optimal Control Problem of Forward-Backward Stochastic Volterra Integral Equations with State Constraints [PDF]
Abstract and Applied Analysis, 2014 This paper is devoted to the stochastic optimal control problems for systems governed by forward-backward stochastic Volterra integral equations (FBSVIEs, for short) with state constraints.
Qingmeng Wei, Xinling Xiao
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Exponential integrators for stochastic Schrödinger equations [PDF]
Physical Review E, 2020 We present a class of exponential integrators to compute solutions of the stochastic Schr dinger equation arising from the modeling of open quantum systems. In order to be able to implement the methods within the same framework as the deterministic counterpart, we express the solution using the Kunita's representation.
Jingze Li, Xiantao Li
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Mathematical modeling and nonlinear bilateral multivalued stochastic integral equations [PDF]
PLoS ONEMarek T. Malinowski
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A singular stochastic integral equation [PDF]
Proceedings of the American Mathematical Society, 1982 This note is devoted to the discussion of the stochastic differential equation X d X + Y d Y = 0 XdX + YdY = 0 , X X and Y Y being continuous local martingales. A method to construct solutions of this equation is given.
Nualart, David, Sanz, Marta
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Stochastic Integral Equations without Probability [PDF]
Bernoulli, 2000 L. C. Young has constructed an extension of the Riemann-Stieltjes integral \(\int_a^b f dh\), where the functions \(f,h:[a,b]\to{\mathbb R}\) have finite \(p\)-variation and finite \(q\)-variation, respectively, with \(p^{-1}+q^{-1}>1\). Motivated by the fact that certain stochastic processes which are not semimartingales may have a bounded \(p ...
Thomas Mikosch +2 more
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Mathematics, 2021 It is well known that Stochastic equations had many useful applications in describing numerous events and problems of real world, and the nonlocal integral condition is important in physics, finance and engineering.
Ahmed M. A. El-Sayed, Hoda A. Fouad
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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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Mathematics, 2021 The fractional stochastic differential equations had many applications in interpreting many events and phenomena of life, and the nonlocal conditions describe numerous problems in physics and finance.
A. M. A. El-Sayed, Hoda A. Fouad
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Известия Иркутского государственного университета: Серия "Математика", 2021 The article considers second-order system of linear stochastic partial differential equations of hyperbolic type with Goursat boundary conditions. Earlier, in a number of papers, representations of the solution Goursat problem for linear stochastic ...
K.B. Mansimov, R.O. Mastaliyev
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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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