Statistical aspects of the fractional stochastic calculus (2006)
Tudor, Ciprian A., Viens, Frederi G.
We apply the techniques of stochastic integration with respect to fractional Brownian motion and the theory of regularity and supremum estimation for stochastic processes to study the maximum...
Analysis of the Rosenblatt process (2006)
We analyze {\em the Rosenblatt process} which is a selfsimilar process with stationary increments and which appears as limit in the so-called {\em Non Central Limit Theorem} (Dobrushin and Major...
Remarks on some linear fractional stochastic equations (2005)
Nourdin, Ivan, Tudor, Ciprian A.
Using the multiple stochastic integrals we prove an existence and uniqueness result for a linear stochastic equation driven by the fractional Brownian motion with any Hurst parameter. We study both...
Anticipating integrals and martingales on the Poisson space (2005)
Peccati, Giovanni, Tudor, Ciprian A.
Let $\tilde{N}\_{t}$ be a standard compensated Poisson process on $[0,1]$. We prove a new characterization of anticipating integrals of the Skorohod type with respect to $\tilde{N}$, and use it to...
Martingale structure of Skorohod integral processes (2005)
Peccati, Giovanni, Thieullen, Michèle, Tudor, Ciprian A.
Let the process Y(t) be a Skorohod integral process with respect to Brownian motion. We use a recent result by Tudor (2004), to prove that Y(t) can be represented as the limit of linear combinations...
Ito Formula and Local Time for the Fractional Brownian Sheet (2003)
Tudor, Ciprian A.; Laboratoire De Probabilit'{e}s, Universit'{e} De Paris 6; Tudor@ccr.jussieu.fr, Viens, Frederi G.; Purdue University; Viens@purdue.edu
Using the techniques of the stochastic calculus of variations for Gaussian processes, we derive an It^{o} formula for the fractional Brownian sheet with Hurst parameters bigger than $1/2$. As an...