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Autor:
Bradley, Richard C.
Consider the class of (functions of) strictly stationary Markov chains in which (i) the second moments are finite and (ii) absolute regularity (beta-mixing) is satisfied with exponential mixing rate. For (functions of) Markov chains in that class tha
Externí odkaz:
http://arxiv.org/abs/2411.03528
Autor:
Bradley, Richard C.
A class of examples is constructed to show that for strictly stationary Markov chains that are reversible, the simultaneous mixing rates for the $\rho$-mixing and strong mixing ($\alpha$-mixing) conditions can be fairly arbitrary, within certain unav
Externí odkaz:
http://arxiv.org/abs/2210.00355
Autor:
Bradley, Richard C.
It has been well known for some time that for strictly stationary Markov chains that are ``reversible'', that special symmetry provides special extra features in the mathematical theory. This paper here is primarily a purely expository review of some
Externí odkaz:
http://arxiv.org/abs/1910.01495
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Autor:
Bradley, Richard C.
A 1963 theorem of P. Cs\'aki and J. Fischer deals with the "maximal correlation coefficient" in the context of independent pairs of $\sigma$-fields on a probability space. Here a somewhat restricted "cousin" of their result is presented for the same
Externí odkaz:
http://arxiv.org/abs/1603.08964
Autor:
Bradley, Richard C., Tone, Cristina
In this paper we extend a central limit theorem of Peligrad for uniformly strong mixing random fields satisfying the Lindeberg condition in the absence of stationarity property. More precisely, we study the asymptotic normality of the partial sums of
Externí odkaz:
http://arxiv.org/abs/1512.01310
Autor:
Bradley, Richard C.
Strictly stationary INAR(1) ("integer-valued autoregressive processes of order 1") with Poisson innovations are "interlaced rho-mixing".
Externí odkaz:
http://arxiv.org/abs/1509.09303
A central limit theorem is proved for some strictly stationary sequences of random variables that satisfy certain mixing conditions and are subjected to the "shrinking operators" $U_r(x):=[\max\{|x|-r,0\}]\cdot x/|x|,\ r \ge 0$. For independent, iden
Externí odkaz:
http://arxiv.org/abs/1410.0214
Autor:
Bradley, Richard C.
It is well known that for a strictly stationary, reversible, Harris recurrent Markov chain, the $\rho$-mixing condition is equivalent to geometric ergodicity and to a "spectral gap" condition. In this note, it will be shown with an example that for t
Externí odkaz:
http://arxiv.org/abs/1403.4895
Publikováno v:
Stat.& Probab. Letters 84, 2014, pp. 67-71
For nonstationary, strongly mixing sequences of random variables taking their values in a finite-dimensional Euclidean space, with the partial sums being normalized via matrix multiplication, with certain standard conditions being met, the possible l
Externí odkaz:
http://arxiv.org/abs/1403.1441