156 citations · 348 across the 12 of their papers we have counts for
13 papers
On the invariance principle for reversible Markov chains
Magda Peligrad, Sergey Utev
In this paper, we investigate the functional central limit theorem for stochastic processes associated to partial sums of additive functionals of reversible Markov chains with gene…
Functional CLT for martingale-like nonstationary dependent structures
Florence Merlevède, Magda Peligrad, Sergey Utev
In this paper we develop non-stationary martingale techniques for dependent data. We shall stress the non-stationary version of the projective Maxwell-Woodroofe condition, which wi…
Optimal bounds for self-intersection local times
George Deligiannidis, Sergey Utev
For a random walk in , let be its local time at the site . Define the -fold self intersection local time $L_n(α) := \sum…
Asymptotic variance of stationary reversible and normal Markov processes
George Deligiannidis, Magda Peligrad, Sergey Utev
We obtain necessary and sufficient conditions for the regular variation of the variance of partial sums of functionals of discrete and continuous-time stationary Markov processes w…
Variance of partial sums of stationary sequences
George Deligiannidis, Sergey Utev
Let be a centred sequence of weakly stationary random variables with spectral measure and partial sums . We show that $\operatorname {var}(…
An asymptotic variance of the self-intersections of random walks
George Deligiannidis, Sergey Utev
We present a Darboux-Wiener type lemma and apply it to obtain an exact asymptotic for the variance of the self-intersection of one and two-dimensional random walks. As a corollary,…