382 research outputs found
Weak convergence of the Stratonovich integral with respect to a class of Gaussian processes
For a Gaussian process and smooth function , we consider a
Stratonovich integral of , defined as the weak limit, if it exists, of a
sequence of Riemann sums. We give covariance conditions on such that the
sequence converges in law. This gives a change-of-variable formula in law with
a correction term which is an It\^o integral of with respect to a
Gaussian martingale independent of . The proof uses Malliavin calculus and a
central limit theorem from [10]. This formula was known for fBm with
[9]. We extend this to a larger class of Gaussian processes.Comment: 39 pages. arXiv admin note: text overlap with arXiv:1105.484
A construction of the rough path above fractional Brownian motion using Volterra's representation
This note is devoted to construct a rough path above a multidimensional
fractional Brownian motion with any Hurst parameter , by means
of its representation as a Volterra Gaussian process. This approach yields some
algebraic and computational simplifications with respect to [Stochastic
Process. Appl. 120 (2010) 1444--1472], where the construction of a rough path
over was first introduced.Comment: Published in at http://dx.doi.org/10.1214/10-AOP578 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Noncentral limit theorem for the generalized Rosenblatt process
We use techniques of Malliavin calculus to study the convergence in law of a
family of generalized Rosenblatt processes with kernels defined by
parameters taking values in a tetrahedral region of \RR^q.
We prove that, as converges to a face of , the process
converges to a compound Gaussian distribution with random variance
given by the square of a Rosenblatt process of one lower rank. The convergence
in law is shown to be stable. This work generalizes a previous result of Bai
and Taqqu, who proved the result in the case and without stability
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