On the lower classes of some mixed fractional Gaussian processes with two logarithmic factors.
On the mixed fractional Brownian motion.
On the Oscillation Functions of Gaussian Processes.
On the persistence of decorrelation in the theory of wave turbulence
We study the statistical properties of the solutions of the Kadomstev-Petviashvili equations (KP-I and KP-II) on the torus when the initial datum is a random variable. We give ourselves a random variable with values in the Sobolev space with big enough such that its Fourier coefficients are independent from each other. We assume that the laws of these Fourier coefficients are invariant under multiplication by for all . We investigate about the persistence of the decorrelation between the...
On the regularity of stochastic currents, fractional brownian motion and applications to a turbulence model
We study the pathwise regularity of the map φ↦I(φ)=∫0T〈φ(Xt), dXt〉, where φ is a vector function on ℝd belonging to some Banach space V, X is a stochastic process and the integral is some version of a stochastic integral defined via regularization. A continuous version of this map, seen as a random element of the topological dual of V will be called stochastic current. We give sufficient conditions for the current to live in some Sobolev space of distributions and we provide elements to conjecture...
On the Supports of Absolutely Continous Gauss Measures on Connected Lie Groups.
On the tail index estimation of an autoregressive Pareto process
In this paper we consider an autoregressive Pareto process which can be used as an alternative to heavy tailed MARMA. We focus on the tail behavior and prove that the tail empirical quantile function can be approximated by a Gaussian process. This result allows to derive a class of consistent and asymptotically normal estimators for the shape parameter. We will see through simulation that the usual estimation procedure based on an i.i.d. setting may fall short of the desired precision.
On the tails of the distribution of the maximum of a smooth stationary gaussian process
We study the tails of the distribution of the maximum of a stationary gaussian process on a bounded interval of the real line. Under regularity conditions including the existence of the spectral moment of order 8, we give an additional term for this asymptotics. This widens the application of an expansion given originally by Piterbarg [11] for a sufficiently small interval.
On the tails of the distribution of the maximum of a smooth stationary Gaussian process
We study the tails of the distribution of the maximum of a stationary Gaussian process on a bounded interval of the real line. Under regularity conditions including the existence of the spectral moment of order 8, we give an additional term for this asymptotics. This widens the application of an expansion given originally by Piterbarg [CITE] for a sufficiently small interval.
On threshold autoregressive processes
On trajectories of Gaussian Markov random fields
On Truncated Variation of Brownian Motion with Drift
We introduce the concept of truncated variation of Brownian motion with drift, which differs from regular variation by neglecting small jumps (smaller than some c > 0). We estimate the expected value of the truncated variation. The behaviour resembling phase transition as c varies is revealed. Truncated variation appears in the formula for an upper bound for return from any trading based on a single asset with flat commission.
On weak brownian motions of arbitrary order
On Weak Convergence Of Spectral Density Estimate
Optimal linear filtering of general multidimensional Gaussian processes and its application to Laplace transforms of quadratic functionals.
Orthogonal decompositions in Hilbert -modules and stationary processes.
Oscillations de fonctions aléatoires gaussiennes à valeurs vectorielles.