Stochastic Calculus with Respect to Free Brownian Motion and Analysis on Wigner Space
نویسنده
چکیده
We deene stochastic integrals with respect to free Brownian motion, and show that they satisfy Burkholder-Gundy type inequalities in operator norm. We prove also a version of It^ o's predictable representation theorem, as well as product form and functional form of It^ o's formula. Finally we develop stochastic analysis on the free Fock space, in analogy with stochastic analysis on the Wiener space.
منابع مشابه
The Effects of Different SDE Calculus on Dynamics of Nano-Aerosols Motion in Two Phase Flow Systems
Langevin equation for a nano-particle suspended in a laminar fluid flow was analytically studied. The Brownian motion generated from molecular bombardment was taken as a Wiener stochastic process and approximated by a Gaussian white noise. Euler-Maruyama method was used to solve the Langevin equation numerically. The accuracy of Brownian simulation was checked by performing a series of simulati...
متن کاملOn time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays
In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory
متن کاملBrownian and fractional Brownian stochastic currents via Malliavin calculus
By using Malliavin calculus and multiple Wiener-Itô integrals, we study the existence and the regularity of stochastic currents defined as Skorohod (divergence) integrals with respect to the Brownian motion and to the fractional Brownian motion. We consider also the multidimensional multiparameter case and we compare the regularity of the current as a distribution in negative Sobolev spaces wit...
متن کاملStochastic Calculus for BrownianMotion on a Brownian FractureBy
(To Appear) Stochastic Calculus for Brownian Motion on a Brownian Fracture By Davar Khoshnevisan* & Thomas M. Lewis University of Utah & Furman University Abstract. The impetus behind this work is a pathwise development of stochastic integrals with respect to iterated Brownian motion. We also provide a detailed analysis of the variations of iterated Brownian motion. These variations are linked ...
متن کاملG–Expectation, G–Brownian Motion and Related Stochastic Calculus of Itô Type
We introduce a notion of nonlinear expectation —-G–expectation—generated by a nonlinear heat equation with a given infinitesimal generator G. We first discuss the notion of G–standard normal distribution. With this nonlinear distribution we can introduce our G–expectation under which the canonical process is a G–Brownian motion. We then establish the related stochastic calculus, especially stoc...
متن کامل