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An Extension of the Stochastic Integral
Annals of Probability, 1982 Two related extensions of the stochastic integral are discussed. These extensions allow the integrand to anticipate the Brownian motion, and arise in the study of linear stochastic integral equations. The development is based on the homogeneous chaos expansion of the integrand.
Marc A Berger
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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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Stratonovich-type integral with respect to a general stochastic measure
Stochastics, 2016 Let $\mu$ be a general stochastic measure, where we assume for $\mu$ only $\sigma$-additivity in probability and continuity of paths. We prove that the symmetric integral $\int_{[0,T]}f(\mu_t, t)\circ\,{\rm d}\mu_t$ is well defined.
V N Radchenko
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Frontiers in Physics, 2022 Let SH be a sub-fractional Brownian motion with index 12<H<1. In this paper, we consider the linear self-interacting diffusion driven by SH, which is the solution to the equationdXtH=dStH−θ(∫0tXtH−XsHds)dt+νdt,X0H=0,where θ < 0 and ν∈R are two ...
Han Gao, Rui Guo, Yang Jin, Litan Yan
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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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On relation between one multiple and a corresponding one-dimensional integral with applications [PDF]
Yugoslav Journal of Operations Research, 2018 For a given finite positive measure on an interval I ⊆ R, a multiple stochastic integral of a Volterra kernel with respect to a product of a corresponding Gaussian orthogonal stochastic measure is introduced.
Bajić Tatjana
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On Convergence to Stochastic Integrals [PDF]
Journal of Theoretical Probability, 2015 20pages
Lin, Zhengyan, Wang, Hanchao
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A generalized white noise space approach to stochastic integration for a class of Gaussian stationary increment processes [PDF]
Opuscula Mathematica, 2013 Given a Gaussian stationary increment processes, we show that a Skorokhod-Hitsuda stochastic integral with respect to this process, which obeys the Wick-Itô calculus rules, can be naturally defined using ideas taken from Hida's white noise space theory ...
Daniel Alpay, Alon Kipnis
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Mathematics, 2023 Controllability is a basic problem in the study of stochastic generalized systems. Compared with ordinary stochastic systems, the structure of stochastic singular systems is more complex, and it is necessary to study the controllability of stochastic ...
Zhaoqiang Ge
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Stochastic variational integrators [PDF]
IMA Journal of Numerical Analysis, 2008 This paper presents a continuous and discrete Lagrangian theory for stochastic Hamiltonian systems on manifolds. The main result is to derive stochastic governing equations for such systems from a critical point of a stochastic action. Using this result the paper derives Langevin-type equations for constrained mechanical systems and implements a ...
Bou-Rabee, Nawaf, Owhadi, Houman
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