Weighted sums of I.I.D. Random variables attracted to integrals of stable processes

作者: Yuji Kasahara , Makoto Maejima

DOI: 10.1007/BF00718037

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摘要: Under the assumption of convergence partial sum processesZ n (t) i.i.d. random variables to an α-stable Levy processZ(σ)(t), 0<α≦2, weighted sums ∫f (u)dZ (u) ∫f(u)dZ(α)(u) is studied. The general result then applied examine domain attraction fractional stable process.

参考文章(18)
Florin Avram, Murad S. Taqqu, Weak Convergence of Moving Averages with Infinite Variance Birkhäuser Boston. pp. 399- 415 ,(1986) , 10.1007/978-1-4615-8162-8_18
Torgny Lindvall, Weak convergence of probability measures and random functions in the function space D[0,∞) Journal of Applied Probability. ,vol. 10, pp. 109- 121 ,(1973) , 10.2307/3212499
William Feller, T. Teichmann, An Introduction to Probability Theory and Its Applications, Vol. 2 Physics Today. ,vol. 20, pp. 76- 76 ,(1967) , 10.1063/1.3034322
Wim Vervaat, Sample Path Properties of Self-Similar Processes with Stationary Increments Annals of Probability. ,vol. 13, pp. 1- 27 ,(1985) , 10.1214/AOP/1176993063
Ward Whitt, Some Useful Functions for Functional Limit Theorems Mathematics of Operations Research. ,vol. 5, pp. 67- 85 ,(1980) , 10.1287/MOOR.5.1.67
Murad S. Taqqu, Robert L. Wolpert, Infinite variance self-similar processes subordinate to a poisson measure Probability Theory and Related Fields. ,vol. 62, pp. 53- 72 ,(1983) , 10.1007/BF00532163
John Lamperti, Semi-stable stochastic processes Transactions of the American Mathematical Society. ,vol. 104, pp. 62- 78 ,(1962) , 10.1090/S0002-9947-1962-0138128-7
Richard Davis, Sidney Resnick, Limit Theory for Moving Averages of Random Variables with Regularly Varying Tail Probabilities Annals of Probability. ,vol. 13, pp. 179- 195 ,(1985) , 10.1214/AOP/1176993074
Makoto Maejima, On a class of self-similar processes Probability Theory and Related Fields. ,vol. 62, pp. 235- 245 ,(1983) , 10.1007/BF00538799