Geodesic
Linear rescaling of the stochastic process
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 2, pp. 277-289 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 60F05, 60G10, 60G18, 60G99, 62E10, 62E20
Keywords: self-similar processes; convergence in distribution 
@article{CMUC_1992_33_2_a7,
     author = {Lachout, Petr},
     title = {Linear rescaling of the stochastic process},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {277--289},
     year = {1992},
     volume = {33},
     number = {2},
     mrnumber = {1189658},
     zbl = {0757.60034},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1992_33_2_a7/}
}
TY  - JOUR
AU  - Lachout, Petr
TI  - Linear rescaling of the stochastic process
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 1992
SP  - 277
EP  - 289
VL  - 33
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/CMUC_1992_33_2_a7/
LA  - en
ID  - CMUC_1992_33_2_a7
ER  - 
%0 Journal Article
%A Lachout, Petr
%T Linear rescaling of the stochastic process
%J Commentationes Mathematicae Universitatis Carolinae
%D 1992
%P 277-289
%V 33
%N 2
%U http://geodesic.mathdoc.fr/item/CMUC_1992_33_2_a7/
%G en
%F CMUC_1992_33_2_a7
Lachout, Petr. Linear rescaling of the stochastic process. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 2, pp. 277-289. http://geodesic.mathdoc.fr/item/CMUC_1992_33_2_a7/

[1] Aczél J.: Lectures on Functional Equations and their Applications. Academic Press, New York, 1966. | MR

[2] Hudson W.H., Mason J.D.: Operator-self-similar processes in a finite-dimensional space. Trans. AMS 273 (1982), 281-297. | MR | Zbl

[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

[5] Lamperti J.: Semi-stable stochastic processes. Trans. Amer. Math. Soc. 104 (1962), 62-78. | MR | Zbl

[6] Vervaat W.: Properties of General Self-Similar Processes. 46th Session of the International Statistical Institute of Tokyo, Japan, 1987. | MR | Zbl

[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 | Zbl