Point processes associated with stationary stable processes

Stochastic Processes and their Applications

Volumn 114, Issue 2, 2004, Pages 191-209

  Resnick, Sidney ^a   Samorodnitsky, Gennady ^a  

^a School of Operations Research and Industrial Engineering   (United States)

Author keywords

Point process; Random measure; Stable process; Stationary process; Vague convergence; Weak convergence

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; INTEGRAL EQUATIONS; MARKOV PROCESSES; MATHEMATICAL MODELS; PROBABILITY; THEOREM PROVING;

LAPLACE FUNCTIONAL; POINT PROCESS; RANDOM MEASURE; STABLE PROCESS; STATIONARY PROCESS; VAGUE CONVERGENCE; WEAK CONVERGENCE;

RANDOM PROCESSES;

EID: 8444240474     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2004.06.004     Document Type: Article

References (12)

1. J. Aaronson, An Introduction to Infinite Ergodic Theory, in: Mathematical Surveys and Monographs, Vol. 50, American Mathematical Society, Providence, RI, 1997.
2. R. Davis, T. Hsing, Point processes for partial sum convergence for weakly dependent random variables with infinite variance, Ann. Probab. 23 (1995) 879-917.
3. R. Davis, S. Resnick, Limit theory for moving averages of random variables with regularly varying tail probabilities, Ann. Probab. 13 (1985) 179-195.
4. T. Harris, H. Robbins, Ergodic theory of Markov chains admitting an infinite invariant measure, Proc. Nat. Acad. Sci. 39 (1953) 860-864.
5. U. Krengel, Ergodic Theorems, De Gruyter, Berlin, 1985.
6. R. LePage, M. Woodroofe, J. Zinn, Convergence of a stable distribution via order statistics, Ann. Probab. 9 (1981) 624-632.
7. T. Mori, Limit distributions of two-dimensional point processes generated by strong mixing sequences, Yokohama Mathematical Journal 25 (1977) 155-168.
8. S. Resnick, Extreme Values, Regular Variation and Point Processes, Springer, Now York, 1987.
9. S. Resnick, G. Samorodnitsky, F. Xue, Growth rates of sample covariances of stationary symmetric α-stable processes associated with null recurrent Markov chains, Stochastic Process. Appl. 85 (2000) 321-339.
10. J. Rosiński, On the structure of stationary stable processes, Ann. Probab. 23 (1995) 1163-1187.
11. G. Samorodnitsky, Extreme value theory, ergodic theory, and the boundary between short memory and long memory for stationary stable processes, Ann. Probab. 32 (2004) 1438-1468.
12. G. Samorodnitsky, M. Taqqu, Stable Non-Gaussian Random Processes, Chapman & Hall, New York, 1994.