A remark on the equivalence of Gaussian processes.
A Simple Proof of the Majorizing Measure Theorem.
A singular parabolic Anderson model.
A transformation from prediction to past of an -stochastic process
A version of the Harris-Spitzer "random constant velocity" model for infinite systems of particles
About the linear-quadratic regulator problem under a fractional brownian perturbation
In this paper we solve the basic fractional analogue of the classical linear-quadratic gaussian regulator problem in continuous time. For a completely observable controlled linear system driven by a fractional brownian motion, we describe explicitely the optimal control policy which minimizes a quadratic performance criterion.
About the linear-quadratic regulator problem under a fractional Brownian perturbation
In this paper we solve the basic fractional analogue of the classical linear-quadratic Gaussian regulator problem in continuous time. For a completely observable controlled linear system driven by a fractional Brownian motion, we describe explicitely the optimal control policy which minimizes a quadratic performance criterion.
Actuarial Approach to Option Pricing in a Fractional Black-Scholes Model with Time-Dependent Volatility
We study actuarial methods of option pricing in a fractional Black-Scholes model with time-dependent volatility. We interpret the option as a potential loss and we show that the fair premium needed to insure this loss coincides with the expectation of the discounted claim payoff under the average risk neutral measure.
Additive Covariance kernels for high-dimensional Gaussian Process modeling
Gaussian Process models are often used for predicting and approximating expensive experiments. However, the number of observations required for building such models may become unrealistic when the input dimension increases. In oder to avoid the curse of dimensionality, a popular approach in multivariate smoothing is to make simplifying assumptions like additivity. The ambition of the present work is to give an insight into a family of covariance kernels that allows combining the features of Gaussian...
Almost sure central limit theorem for a nonstationary Gaussian sequence.
Almost-sure path properties of fractional brownian sheet
An almost sure limit theorem for the maxima of strongly dependent Gaussian sequences.
An approach to the stochastic calculus in the non-Gaussian case.
An asymptotic bound for the tail of the distribution of the maximum of a gaussian process
An asymptotic test for quantitative gene detection
An extension of the Clark-Ocone formula.
An infinite dimensional central limit theorem for correlated martingales
An Itô type isometry for loops in via the brownian bridge
An optimal property of the best linear unbiased interpolation filter
Analyse asymptotique des processus gaussiens stationnaires