6 papers
Asymptotic accuracy in estimation of a fractional signal in a small white noise
M. Kleptsyna, D. Marushkevych, P. Chigansky
This paper revisits the problem of estimating the fractional Ornstein - Uhlenbeck process observed in a linear channel with white noise of small intensity. We drive the exact asymp…
On the fundamental solution of heat and stochastic heat equations
Marina Kleptsyna, Andrey Piatnitski, Alexandre Popier
We consider the generic divergence form second order parabolic equation with coefficients that are regular in the spatial variables and just measurable in time. We show that the sp…
Mixed fractional Brownian motion: a spectral take
P. Chigansky, M. Kleptsyna, D. Marushkevych
This paper provides yet another look at the mixed fractional Brownian motion (fBm), this time, from the spectral perspective. We derive an approximation for the eigenvalues of its…
Exact spectral asymptotics of fractional processes
P. Chigansky, M. Kleptsyna, D. Marushkevych
Eigenproblems frequently arise in theory and applications of stochastic processes, but only a few have explicit solutions. Those which do, are usually solved by reduction to the ge…
Gärtner-Ellis condition for squared asymptotically stationary Gaussian processes
Marina Kleptsyna, Alain Le Breton, Bernard Ycart
The Gärtner-Ellis condition for the square of an asymptotically stationary Gaussian process is established. The same limit holds for the conditional distri-bution given any fixed i…
Asymptotic properties of the MLE for the autoregressive process coefficients under stationary Gaussian noise
Alexandre Brouste, Chunhao Cai, Marina Kleptsyna
In this paper we are interested in the Maximum Likelihood Estimator (MLE) of the vector parameter of an autoregressive process of order with regular stationary Gaussian noise.…