Displaying similar documents to “Stochastic affine evolution equations with multiplicative fractional noise”

Stochastic evolution equations driven by Liouville fractional Brownian motion

Zdzisław Brzeźniak, Jan van Neerven, Donna Salopek (2012)

Czechoslovak Mathematical Journal

Similarity:

Let H be a Hilbert space and E a Banach space. We set up a theory of stochastic integration of ℒ ( H , E ) -valued functions with respect to H -cylindrical Liouville fractional Brownian motion with arbitrary Hurst parameter 0 < β < 1 . For 0 < β < 1 2 we show that a function Φ : ( 0 , T ) → ℒ ( H , E ) is stochastically integrable with respect to an H -cylindrical Liouville fractional Brownian motion if and only if it is stochastically integrable with respect to an H -cylindrical fractional Brownian motion. We apply our results to stochastic...

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...

Deterministic characterization of viability for stochastic differential equation driven by fractional brownian motion

Tianyang Nie, Aurel Răşcanu (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

In this paper, using direct and inverse images for fractional stochastic tangent sets, we establish the deterministic necessary and sufficient conditions which control that the solution of a given stochastic differential equation driven by the fractional Brownian motion evolves in some particular sets . As a consequence, a comparison theorem is obtained.

Kolmogorov equation and large-time behaviour for fractional Brownian motion driven linear SDE's

Michal Vyoral (2005)

Applications of Mathematics

Similarity:

We consider a stochastic process X t x which solves an equation d X t x = A X t x d t + Φ d B t H , X 0 x = x where A and Φ are real matrices and B H is a fractional Brownian motion with Hurst parameter H ∈ ( 1 / 2 , 1 ) . The Kolmogorov backward equation for the function u ( t , x ) = 𝔼 f ( X t x ) is derived and exponential convergence of probability distributions of solutions to the limit measure is established.

Stochastic integration of functions with values in a Banach space

J. M. A. M. van Neerven, L. Weis (2005)

Studia Mathematica

Similarity:

Let H be a separable real Hilbert space and let E be a real Banach space. In this paper we construct a stochastic integral for certain operator-valued functions Φ: (0,T) → ℒ(H,E) with respect to a cylindrical Wiener process W H ( t ) t ∈ [ 0 , T ] . The construction of the integral is given by a series expansion in terms of the stochastic integrals for certain E-valued functions. As a substitute for the Itô isometry we show that the square expectation of the integral equals the radonifying norm of an operator...