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Keywords:
self-similar processes; convergence in distribution
self-similar processes; convergence in distribution
Summary:
Discussion on the limits in distribution of processes $Y$ under joint rescaling of space and time is presented in this paper. The results due to Lamperti (1962), Weissman (1975), Hudson & Mason (1982) and Laha & Rohatgi (1982) are improved here.
References:
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[2] Hudson W.H., Mason J.D.: Operator-self-similar processes in a finite-dimensional space. Trans. AMS 273 (1982), 281-297. MR 0664042 | Zbl 0508.60044
[3] Jarník V.: Differential Calculus II (in Czech). Academia, Prague, 1976.
[4] Laha R.G., Rohatgi V.K.: Operator self similar stochastic processes in $R_+^d$. Stochastic Process. Appl. 12 (1982), 73-84. MR 0632393
[5] Lamperti J.: Semi-stable stochastic processes. Trans. Amer. Math. Soc. 104 (1962), 62-78. MR 0138128 | Zbl 0286.60017
[6] Vervaat W.: Properties of General Self-Similar Processes. 46th Session of the International Statistical Institute of Tokyo, Japan, 1987. MR 1027195 | Zbl 0813.60041
[7] Weissman I.: On location and scale functions of a class of limiting processes with application to extreme value theory. Ann. Probab. 3 (1975), 178-181. MR 0362458 | Zbl 0303.60021
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