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Statistical inference for stochastic parabolic equations: a spectral approach.

S. V. Lototsky (2009)

Publicacions Matemàtiques

Stochastic calculus with respect to fractional Brownian motion

David Nualart (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

Fractional Brownian motion (fBm) is a centered self-similar Gaussian process with stationary increments, which depends on a parameter $H \in (0, 1)$ 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 respect to fBm:...

Stochastic convolution in separable Banach spaces and the stochastic linear Cauchy problem

Zdzisław Brzeźniak, Jan van Neerven (2000)

Studia Mathematica

Let H be a separable real Hilbert space and let E be a separable real Banach space. We develop a general theory of stochastic convolution of ℒ(H,E)-valued functions with respect to a cylindrical Wiener process ${W_{t}^{H}}_{t \in [0, T]}$ with Cameron-Martin space H. This theory is applied to obtain necessary and sufficient conditions for the existence of a weak solution of the stochastic abstract Cauchy problem (ACP) $d X_{t} = A X_{t} d t + B d W_{t}^{H}$ (t∈ [0,T]), $X_{0} = 0$ almost surely, where A is the generator of a $C_{0}$ -semigroup ${S (t)}_{t \geq 0}$ of bounded linear operators on...

Stochastic integral of divergence type with respect to fractional brownian motion with Hurst parameter $H \in (0, \frac{1}{2})$

Patrick Cheridito, David Nualart (2005)

Annales de l'I.H.P. Probabilités et statistiques

Stochastic integration with respect to fractional brownian motion

Philippe Carmona, Laure Coutin, Gérard Montseny (2003)

Annales de l'I.H.P. Probabilités et statistiques

Stochastic integration with respect to Volterra processes

L. Decreusefond (2005)

Annales de l'I.H.P. Probabilités et statistiques

Strong approximations of bivariate uniform empirical processes

Nathalie Castelle, Françoise Laurent-Bonvalot (1998)

Annales de l'I.H.P. Probabilités et statistiques

Subgaussian random variables in Hilbert spaces

Rita Giuliano Antonini (1997)

Rendiconti del Seminario Matematico della Università di Padova

Sufficient conditions for the continuity of stationary gaussian processes and applications to random series of functions

Naresh C. Jain, Michael B. Marcus (1974)

Annales de l'institut Fourier

Let ${X (t), t \in [0, 1]^{n}}$ be a stochastically continuous, separable, Gaussian process with $E [X (t + h) - X (t)]^{2} = σ^{2} (| h |)$ . A sufficient condition, in terms of the monotone rearrangement of $σ$ , is obtained for $X (t)$ to have continuous sample paths almost surely. This result is applied to a wide class of random series of functions, in particular, to random Fourier series.