On a Condition of Almost Markov Regularity

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Previous article Next article On a Condition of Almost Markov RegularityV. A. StatulyavichusV. A. Statulyavichushttps://doi.org/10.1137/1128030PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] B. Ryauba, The central limit theorem for sums of series of weakly dependent random variables, Litovsk. Mat. Sb., 2 (1962), 193–205, (In Russian.) 29:6526 Google Scholar[2] I. G. Zhurbenko, On the estimation of mixed cumulants for a class of random processes, Theory Prob. Appl., 15 (1970), 525–528 LinkGoogle Scholar[3] I. G. Zhurbenko, On strong estimates of mixed cumulants of random processes, Siberian Math. J., 13 (1972), 302–303 CrossrefGoogle Scholar[4] I. G. Zhurbenko and , N. M. Zuev, The higher spectral densities of stationary processes with mixing, Ukrain. Mat. Ž., 27 (1975), 452–463, 572 53:14620 0325.60039 Google Scholar[5] I. G. Zhurbenko, Mixing conditions and asymptotic theory of stationary time seriesStochastic processes and related topics (Proc. Summer Res. Inst. on Statist. Inference for Stochastic Processes, Indiana Univ., Bloomington, Ind., 1974, Vol. 1; dedicated to Jerzy Neyman), Academic Press, New York, 1975, 259–265 51:9177 0349.60031 Google Scholar[6] V. A. Statulyavichus, Limit theorems for random functions. I, Litovsk. Mat. Sb., 10 (1970), 583–592, (In Russian.) 43:2765 Google Scholar[7] V. A. Statulyavichus, Limit theorems for dependent random variables under various regularity conditions, Proceedings of the International Congress of Mathematicians (Vancouver, B. C., 1974), Vol. 2, Canad. Math. Congress, Montreal, Que., 1975, 173–181 55:1420 Google Scholar[8] V. A. Statulyavichus, Application of semi-invariants to asymptotic analysis of distributions of random processesMultivariate analysis, IV (Proc. Fourth Internat. Sympos., Dayton, Ohio, 1975), North-Holland, Amsterdam, 1977, 325–337 57:1614 Google Scholar[9] R. L. Dobrushin, The description of a random field by means of conditional probabilities and conditions for its regularity, Theory Prob. Appl., 13 (1968), 197–224 LinkGoogle Scholar[10] I. A. Ibragimov, Some limit theorems for stationary processes, Theory Prob. Appl., 7 (1962), 349–382 LinkGoogle Scholar[11] M. Rosenblatt, Some remarks on a mixing condition, Ann. Probab., 7 (1979), 170–172 80k:60071a 0925.60052 CrossrefGoogle Scholar[12] V. A. Statulyavichus, Large-deviation theorems for sums of dependent random variables, Lithuanian Math. J., 19 (1979), 289–295 CrossrefGoogle Scholar[13] A. V. Bulinskii, Limit Theorems for Random Processes and Fields, MGU, Moscow, 1981, (In Russian.) Google Scholar[14] V. Statulyavichus, On limit theorems for dependent random variables, Abstracts of Communications of the Third International Vilnius Conference on Probability Theory and Mathematical Statistics, Vilnius: In-t matem. i kibern. AN Lit SSR, 1981, 320–323 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails An Almost-Markov-Type Mixing Condition and Large Deviations for Boolean Models on the LineActa Applicandae Mathematicae, Vol. 96, No. 1-3 | 23 March 2007 Cross Ref Approximation of Distributions of Sums of Weakly Dependent Random Variables by the Normal DistributionLimit Theorems of Probability Theory | 1 Jan 2000 Cross Ref Limit Theorems on Large DeviationsLimit Theorems of Probability Theory | 1 Jan 2000 Cross Ref Every “lower psi-mixing” Markov chain is “interlaced rho-mixing”Stochastic Processes and their Applications, Vol. 72, No. 2 | 1 Dec 1997 Cross Ref Random fields: Applications in cell biologyStochastic Spatial Processes | 16 September 2006 Cross Ref Volume 28, Issue 2| 1984Theory of Probability & Its Applications219-469 History Submitted:10 January 1983Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1128030Article page range:pp. 379-383ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics