Multidimensional bifractional Brownian motion: Ito and Tanaka formulas
نویسندگان
چکیده
Using the Malliavin calculus with respect to Gaussian processes and the multiple stochastic integrals we derive Itô’s and Tanaka’s formulas for the d-dimensional bifractional Brownian motion. 2000 AMS Classification Numbers: 60G12, 60G15, 60H05, 60H07.
منابع مشابه
A decomposition of the bifractional Brownian motion and some applications
In this paper we show a decomposition of the bifractional Brownian motion with parameters H,K into the sum of a fractional Brownian motion with Hurst parameter HK plus a stochastic process with absolutely continuous trajectories. Some applications of this decomposition are discussed.
متن کاملSample Path Properties of Bifractional Brownian Motion
Let B = { B(t), t ∈ R+ } be a bifractional Brownian motion in R. We prove that B is strongly locally nondeterministic. Applying this property and a stochastic integral representation of B , we establish Chung’s law of the iterated logarithm for B , as well as sharp Hölder conditions and tail probability estimates for the local times of B . We also consider the existence and the regularity of th...
متن کاملAn Extension of Bifractional Brownian Motion
In this paper we introduce and study a self-similar Gaussian process that is the bifractional Brownian motion BH,K with parameters H ∈ (0, 1) and K ∈ (1, 2) such that HK ∈ (0, 1). A remarkable difference between the case K ∈ (0, 1) and our situation is that this process is a semimartingale when 2HK = 1.
متن کاملOn the bifractional Brownian motion
This paper is devoted to analyze several properties of the bifractional Brownian motion introduced by Houdré and Villa. This process is a self-similar Gaussian process depending on two parameters H and K and it constitutes a natural generalization of the fractional Brownian motion (which is obtained for K = 1). We adopt the strategy of the stochastic calculus via regularization. Particular inte...
متن کاملCentral Limit Theorem for a Stratonovich Integral with Malliavin Calculus
The purpose of this paper is to establish the convergence in law of the sequence of “midpoint” Riemann sums for a stochastic process of the form f ′(W ), where W is a Gaussian process whose covariance function satisfies some technical conditions. As a consequence we derive a change-ofvariable formula in law with a second order correction term which is an Itô integral of f ′′(W ) with respect to...
متن کامل