Results 1 to 10 of about 34,146 (315)

A note on Kurzweil-Henstock's anticipating non-stochastic integral [PDF]

Mathematica Bohemica
Motivated by the study of anticipating stochastic integrals using Kurzweil-Henstock approach, we use anticipating interval-point pairs (with the tag as the right-end point of the interval) in studying non-stochastic integral, which we call the Kurzweil ...
Yu Xin Ng, Tin Lam Toh
doaj   +3 more sources

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
exaly   +3 more sources

Stochastic Volterra integral equations with a parameter

Advances in Difference Equations, 2017
In this paper, we study the properties of continuity and differentiability of solutions to stochastic Volterra integral equations and backward stochastic Volterra integral equations depending on a parameter.
Yanqing Wang
doaj   +2 more sources

Large Time Behavior on the Linear Self-Interacting Diffusion Driven by Sub-Fractional Brownian Motion With Hurst Index Large Than 0.5 I: Self-Repelling Case

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
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

On Convergence to Stochastic Integrals [PDF]

Journal of Theoretical Probability, 2015
20pages
Lin, Zhengyan, Wang, Hanchao
openaire   +3 more sources

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
doaj   +1 more source

Controllability of Semilinear Stochastic Generalized Systems in Hilbert Spaces by GE-Evolution Operator Method

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
doaj   +1 more source

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
openaire   +3 more sources