Some examples and results in the theory of mixing and random-sum central limit theorems

[1]  M. Kac,et al.  On the Distribution of Values of Sums of the Type Σf(2 k t) , 1946 .

[2]  Wolfgang Richter.  Übertragung von Grenzaussagen für Folgen zufälliger Elemente auf Folgen mit zufälligen Indizes , 1965 .

[3]  M. Csörgo,et al.  Departure from independence: The strong law, standard and random-sum central limit theorems , 1970 .

[4]  Miklós Csörgő,et al.  On the strong law of large numbers and the central limit theorem for martingales , 1968 .

[5]  W. Doeblin.  Sur deux problèmes de M. Kolmogoroff concernant les chaînes dénombrables , 1938 .

[6]  Galen R. Shorack,et al.  Weak Convergence and a Chernoff-Savage Theorem for Random Sample Sizes , 1968 .

[7]  P. Billingsley,et al.  The Lindeberg-Lévy theorem for martingales , 1961 .

[8]  Helen Wittenberg.  Limiting distributions of random sums of independent random variables , 1964 .

[9]  W. Richter.  Limit Theorems for Sequences of Random Variables with Sequences of Random Indeces , 1965 .

[10]  A. Rényi.  On the central limit theorem for the sum of a random number of independent random variables , 1963 .

[11]  D. Menchoff,et al.  Sur les séries de fonctions orthogonales , 1923 .

[12]  A. Rényi.  On mixing sequences of sets , 1958 .

[13]  D. L. Hanson,et al.  On the strong law of large numbers for a class of stochastic processes , 1963 .

[14]  B. Gnedenko.  Sur La Distribution Limite Du Terme Maximum D'Une Serie Aleatoire , 1943 .

[15]  R. Salem,et al.  On Lacunary Trigonometric Series. , 1932, Proceedings of the National Academy of Sciences of the United States of America.

[16]  Patrick Billingsley,et al.  Limit Theorems for Randomly Selected Partial Sums , 1962 .

[17]  W. Hoeffding.  A Class of Statistics with Asymptotically Normal Distribution , 1948 .

[18]  J. Hájek.  Some Extensions of the Wald-Wolfowitz-Noether Theorem , 1961 .

[19]  J. Mogyoródi.  A remark on stable sequences of random variables and a limit distribution theorem for a random sum of independent random variables , 1966 .

[20]  H. Kesten,et al.  On rapidly mixing transformations and an application to continued fractions , 1958 .

[21]  F. J. Anscombe,et al.  Large-sample theory of sequential estimation , 1949, Mathematical Proceedings of the Cambridge Philosophical Society.

[22]  I. Ibragimov,et al.  A Central Limit Theorem for a Class of Dependent Random Variables , 1963 .

[23]  S. Guiasu.  On the Asymptotic Distribution of the Sequences of Random Variables with Random Indices , 1971 .

[24]  D. L. Hanson,et al.  On the central limit theorem for the sum of a random number of independent random variables , 1963 .

[25]  A. Rényi,et al.  On mixing sequences of random variables , 1958 .

[26]  A. Rényi,et al.  On the asymptotic distribution of the sum of a random number of independent random variables , 1957 .

[27]  ON MIXING AND THE CENTRAL LIMIT THEOREM , 1971 .

[28]  W. Rudin.  Trigonometric Series with Gaps , 1960 .

[29]  M. Sreehari.  A limit theorem for the maximum of cumulative sums , 1968 .