12 citations · 26 across the 9 of their papers we have counts for
10 papers
Weighted Nuclear Elastic Net Estimation of (Near-) Low-Rank Drift Matrices in Ornstein-Uhlenbeck Processes
Dmytro Marushkevych, Francisco Pina, Mark Podolskij
We study estimation of the drift matrix in a continuously observed high-dimensional Ornstein-Uhlenbeck process when the drift is exactly or approximately low rank. In this setting,…
Consistent support recovery for high-dimensional diffusions
Dmytro Marushkevych, Francisco Pina, Mark Podolskij
Statistical inference for stochastic processes has advanced significantly due to applications in diverse fields, but challenges remain in high-dimensional settings where parameters…
On Lasso estimator for the drift function in diffusion models
Gabriela Ciolek, Dmytro Marushkevych, Mark Podolskij
In this paper we study the properties of the Lasso estimator of the drift component in the diffusion setting. More specifically, we consider a multivariate parametric diffusion mod…
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 Dantzig and Lasso estimators of the drift in a high dimensional Ornstein-Uhlenbeck model
Gabriela Ciolek, Dmytro Marushkevych, Mark Podolskij
In this paper we present new theoretical results for the Dantzig and Lasso estimators of the drift in a high dimensional Ornstein-Uhlenbeck model under sparsity constraints. Our fo…
Limit behaviour of the minimal solution of a BSDE in the non Markovian setting
Dmytro Marushkevych, Alexandre Popier
We use the functional It{ô} calculus to prove that the solution of a BSDE with singular terminal condition is continuous at the terminal time. Hence we extend known results for a n…
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…
Large deviations for drift parameter estimator of mixed fractional Ornstein--Uhlenbeck process
Dmytro Marushkevych
We investigate large deviation properties of the maximum likelihood drift parameter estimator for Ornstein--Uhlenbeck process driven by mixed fractional Brownian motion.