stochastic integral

stochastic integral

[stō′kas·tik ′int·ə·grəl]
(mathematics)
An integral used to construct the sample functions of a general diffusion process from those of a Wiener process; it has the form where {Wt , t ≥ 0} is a Wiener process, dWt represents the random disturbances occurring in an infinitesimal time interval dt, and at is independent of future disturbances. Also known as Itô's integral.
References in periodicals archive ?
The two most commonly used stochastic integral types are the Ito integral (Ito 1951) and the Stratonovich integral (Stratonovich 1966).
They cover the stochastic integral and Itf formula,Ornstein-Uhlenbeck processes and stochastic differential equations, and random attractors.
infinity]] (I, E) in the sense that it satisfies the following stochastic integral equation:
In this case, the main problem is a concept of a fuzzy stochastic integral which should cover the notion of the classical stochastic Ito integral.
in which X is a real martingale and Y is the stochastic integral, with respect to X, of a certain predictable process H = [([H.
Nayak, Pattanayak and Mishra [1] proved that the random Fourier-Stieltjes series(RFS) (1 ) converges in probability to the stochastic integral
Since the stochastic integral on the right-hand side of Eq.
2]), in paper [1] we could avoid the use of the stochastic integral to obtain some results from stochastic calculus, e.
X [OMEGA] [right arrow] X, x [member of] X, satisfying the stochastic integral equation:
He will present, "FastSies: A Fast Stochastic Integral Equation Solver for Modeling the Rough Surface Effects," during the Silicon Valley Chapter of the IEEE Solid State Circuits Society Monday, May 15, at 7 p.
On the other hand as far as we know there are only few papers dealing with stochastic integral inclusions driven by random fields (see [25], [26], [47]).
The forward looking stochastic integral in discrete time of a process H with respect to a process S is defined by

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