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pro vyhledávání: '"Volny, Dalibor"'
The now classical convergence in distribution theorem for well normalized sums ofstationary martingale increments has been extended to multi-indexed martingaleincrements (see Voln\'{y} (2019) and references in there). In the presentarticle we make pr
Externí odkaz:
http://arxiv.org/abs/2405.14447
Autor:
Volny, Dalibor
Publikováno v:
Stochastics and DynamicsVol. 06, No. 02, pp. 173-183 (2006)
We generalise the martingale-coboundary representation of discrete time stochastic processes to the non-stationary case and to random variables in Orlicz spaces. Related limit theorems (CLT, invariance principle, log log law, probabilities of large d
Externí odkaz:
http://arxiv.org/abs/2311.03134
Autor:
Kosloff, Zemer, Volný, Dalibor
We show that alpha stable L\'evy motions can be simulated by any ergodic and aperiodic probability preserving transformation. Namely we show: - for $0<\alpha<1$ and every $\alpha$ stable L\'evy motion $\mathbb{W}$, there exists a function f whose par
Externí odkaz:
http://arxiv.org/abs/2309.05753
Publikováno v:
Comptes Rendus. Math\'ematique, Tome 361 (2023), pp. 1511-1519
In this note, we investigate the convergence of a $U$-statistic of order two having stationary ergodic data. We will find sufficient conditions for the almost sure and $L^1$ convergence and present some counter-examples showing that the $U$-statistic
Externí odkaz:
http://arxiv.org/abs/2302.04539
Autor:
Kosloff, Zemer, Volny, Dalibor
We show that for every ergodic and aperiodic probability preserving transformation and $\alpha\in (0,2)$ there exists a function whose associated time series is in the standard domain of attraction of a non-degenerate symmetric $\alpha$-stable distri
Externí odkaz:
http://arxiv.org/abs/2211.03448
Autor:
Kosloff, Zemer, Volny, Dalibor
We show that for every ergodic and aperiodic probability preserving system, there exists a $\mathbb{Z}$ valued, square integrable function $f$ such that the partial sums process of the time series $\left\{f\circ T^i\right\}_{i=0}^\infty$ satisfies th
Externí odkaz:
http://arxiv.org/abs/1905.05164
We study limit theorems for partial sums of instantaneous functions of a homogeneous Markov chain on a general state space. The summands are heavy-tailed and the limits are stable distributions. The conditions imposed on the transition operator $P$ o
Externí odkaz:
http://arxiv.org/abs/1808.04329
Autor:
Volny, Dalibor
We prove a central limit theorem for stationary multiple (random) fields of martingale differences $f\circ T_{\underline{i}}$, $\underline{i}\in \Bbb Z^d$, where $T_{\underline{i}}$ is a $\Bbb Z^d$ action. In most cases the multiple (random) fields o
Externí odkaz:
http://arxiv.org/abs/1803.09100
Autor:
Peligrad, Magda, Volný, Dalibor
In this paper we study the central limit theorem and its functional form for random fields which are not started from their equilibrium, but rather under the measure conditioned by the past sigma field. The initial class considered is that of orthoma
Externí odkaz:
http://arxiv.org/abs/1802.09106
Autor:
Volny, Dalibor
We prove a martingale-coboundary representation for random fields with a completely commuting filtration. For random variables in L2 we present a necessary and sufficient condition which is a generalization of Heyde's condition for one dimensional pr
Externí odkaz:
http://arxiv.org/abs/1706.07978