44 citations · 81 across the 22 of their papers we have counts for
22 papers
Homogenization of nonlocal equations in randomly evolving media. Diffusion approximation
Marina Kleptsyna, Andrey Piatnitski, Alexandre Popier
The paper deals with homogenization and higher order approximations of solutions to nonlocal evolution equations of convolution type whose coefficients are periodic in the spatial…
How smooth is the drift of the mixed fractional Brownian motion?
Pavel Chigansky, Marina Kleptsyna
The mixed fractional Brownian motion - the sum of independent fractional and standard Brownian motions - is known to be a semimartingale if the Hurst exponent of its fractional…
Asymptotic analysis of the finite predictor for fractional Gaussian noise
P. Chigansky, M. Kleptsyna
This paper proposes a new approach to the asymptotic analysis of the finite predictor for stationary sequences. Our method yields the exact asymptotics of both the relative predict…
Asymptotic analysis in problems with fractional processes
P. Chigansky, M. Kleptsyna
Some problems in the theory and applications of stochastic processes can be reduced to solving integral equations. While explicit solutions for these equations are often elusive, v…
Estimation of the Hurst parameter from continuous noisy data
P. Chigansky, M. Kleptsyna
This paper addresses the problem of estimating the Hurst exponent of the fractional Brownian motion from continuous time noisy sample. Consistent estimation in the setup under cons…
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…
Asymptotic decomposition of solutions to parabolic equations with a random microstructure
Marina Kleptsyna, Andrey Piatnitski, Alexandre Popier
We consider a Cauchy problem for a divergence form second order parabolic operator with rapidly oscillating coefficients that are periodic in spatial variables and random stationar…
Sharp asymptotics in a fractional Sturm-Liouville problem
P. Chigansky, M. Kleptsyna
The current research of fractional Sturm-Liouville boundary value problems focuses on the qualitative theory and numerical methods, and much progress has been recently achieved in…
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…
On the eigenproblem for Gaussian bridges
P. Chigansky, M. Kleptsyna, D. Marushkevych
Spectral decomposition of the covariance operator is one of the main building blocks in the theory and applications of Gaussian processes. Unfortunately it is notoriously hard to d…
Higher order homogenization for random non-autonomous parabolic operators
Marina Kleptsyna, Andrey Piatnitski, Alexandre Popier
We consider Cauchy problem for a divergence form second order parabolic operator with rapidly oscillating coefficients that are periodic in spatial variables and random stationary…
Exact asymptotics in eigenproblems for fractional Brownian covariance operators
Pavel Chigansky, Marina Kleptsyna
Many results in the theory of Gaussian processes rely on the eigenstructure of the covariance operator. However, eigenproblems are notoriously hard to solve explicitly and closed f…
Statistical analysis of the mixed fractional Ornstein--Uhlenbeck process
Pavel Chigansky, Marina Kleptsyna
This paper addresses the problem of estimating drift parameter of the Ornstein - Uhlenbeck type process, driven by the sum of independent standard and fractional Brownian motions.…
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…
On robustness of discrete time optimal filters
Marina Kleptsyna, Alexander Veretennikov
A new result on stability of an optimal nonlinear filter with respect to small perturbations on every step is established.
Exponential transform of quadratic functional and multiplicative ergodicity of a Gauss-Markov process
Marina Kleptsyna, Alain Le Breton, Bernard Ycart
The Laplace transform of partial sums of the square of a non-centered Gauss-Markov process, conditioning on its starting point, is explicitly computed. The parameters of multiplica…
Homogenization of random parabolic operators. Diffusion approximation
Marina Kleptsyna, Andrey Piatnitski, Alexandre Popier
The paper deals with homogenization of divergence form second order parabolic operators whose coefficients are periodic in spatial variables and random stationary in time. Under pr…
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.…
Mixed Gaussian processes: A filtering approach
Chunhao Cai, Pavel Chigansky, Marina Kleptsyna
This paper presents a new approach to the analysis of mixed processes \[X_t=B_t+G_t,\qquad t\in[0,T],\] where is a Brownian motion and is an independent centered Gaussi…
Filtering problems with exponential criteria for general Gaussian signals
M. L. Kleptsyna, A. Le Breton, M. Viot
The explicit solution of the discrete time filtering problems with exponential criteria for a general Gaussian signal is obtained through an approach based on a conditional Cameron…