Displaying similar documents to “Fractional Ornstein-Uhlenbeck processes.”

Stochastic calculus with respect to fractional Brownian motion

David Nualart (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

Similarity:

Fractional Brownian motion (fBm) is a centered self-similar Gaussian process with stationary increments, which depends on a parameter H ∈ ( 0 , 1 ) called the Hurst index. In this conference we will survey some recent advances in the stochastic calculus with respect to fBm. In the particular case H = 1 / 2 , the process is an ordinary Brownian motion, but otherwise it is not a semimartingale and Itô calculus cannot be used. Different approaches have been introduced to construct stochastic integrals with...

Differential equations driven by fractional Brownian motion.

David Nualart, Aurel Rascanu (2002)

Collectanea Mathematica

Similarity:

A global existence and uniqueness result of the solution for multidimensional, time dependent, stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/2 is proved. It is shown, also, that the solution has finite moments. The result is based on a deterministic existence and uniqueness theorem whose proof uses a contraction principle and a priori estimates.

Approximation of the fractional Brownian sheet Ornstein-Uhlenbeck sheet

Laure Coutin, Monique Pontier (2007)

ESAIM: Probability and Statistics

Similarity:

A stochastic “Fubini” lemma and an approximation theorem for integrals on the plane are used to produce a simulation algorithm for an anisotropic fractional Brownian sheet. The convergence rate is given. These results are valuable for any value of the Hurst parameters ( α 1 , α 2 ) ∈ ] 0 , 1 [ 2 , α i ≠ 1 2 . Finally, the approximation process is iterative on the quarter plane ℝ + 2 . A sample of such simulations can be used to test estimators of the parameters = 1,2.