Weak Lévy–Khintchine representation for weak infinite divisibility
Teoriâ veroâtnostej i ee primeneniâ, Tome 60 (2015) no. 1, pp. 131-149 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

@article{TVP_2015_60_1_a5,
     author = {B. H. Jasiulis-Goldyn and J. K. Misiewicz},
     title = {Weak {L\'evy{\textendash}Khintchine} representation for weak infinite divisibility},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {131--149},
     year = {2015},
     volume = {60},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2015_60_1_a5/}
}
TY  - JOUR
AU  - B. H. Jasiulis-Goldyn
AU  - J. K. Misiewicz
TI  - Weak Lévy–Khintchine representation for weak infinite divisibility
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2015
SP  - 131
EP  - 149
VL  - 60
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TVP_2015_60_1_a5/
LA  - en
ID  - TVP_2015_60_1_a5
ER  - 
%0 Journal Article
%A B. H. Jasiulis-Goldyn
%A J. K. Misiewicz
%T Weak Lévy–Khintchine representation for weak infinite divisibility
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2015
%P 131-149
%V 60
%N 1
%U http://geodesic.mathdoc.fr/item/TVP_2015_60_1_a5/
%G en
%F TVP_2015_60_1_a5
B. H. Jasiulis-Goldyn; J. K. Misiewicz. Weak Lévy–Khintchine representation for weak infinite divisibility. Teoriâ veroâtnostej i ee primeneniâ, Tome 60 (2015) no. 1, pp. 131-149. http://geodesic.mathdoc.fr/item/TVP_2015_60_1_a5/

[1] Cambanis S., Keener R., Simons G., “On $\alpha$-symmetric distributions”, J. Multivariate Anal., 13 (1983), 213–233 | MR | Zbl

[2] Dudley R. M., Real Analysis and Probability, Wadsworth Brooks/Cole Advanced Books Software, Wadsworth Inc., Belmont, Ca., 1989 | MR | Zbl

[3] Feller W., An Introduction to Probability Theory and its Applications, v. 2, John Wiley, New York, 1966 | MR | Zbl

[4] Jasiulis B. H., “Limit property for regular and weak generalized convolution”, J. Theoret. Probab., 23:1 (2010), 315–327 | MR | Zbl

[5] Jasiulis-Goldyn B. H., Misiewicz J. K., “On the uniqueness of the Kendall generalized convolution”, J. Theoret. Probab., 24:3 (2011), 746–755 | DOI | MR | Zbl

[6] Kelker D., “Infinite divisibility and variance mixtures of the normal distribution”, Ann. Math. Statist., 42:2 (1971), 802–808 | DOI | MR | Zbl

[7] Kingman J. F. C., “Random walks with spherical symmetry”, Acta Math., 109:1 (1963), 11–53 | DOI | MR | Zbl

[8] Kucharczak J., Urbanik K., “Quasi-stable functions”, Bull. Polon. Acad. Sci. Ser. Sci. Math. Astronom. Phys., 22:3 (1974), 263–268 | MR | Zbl

[9] Kucharczak J., Urbanik K., “Transformations preserving weak stability”, Bull. Polon. Acad. Sci. Ser. Sci. Math. Astronom. Phys., 34:7–8 (1986), 475–486 | MR | Zbl

[10] Lukács E., Characteristic Functions, Griffin, London, 1960 | Zbl

[11] Mazurkiewicz G., “On the infinite divisibility of scale mixtures of symmetric $\alpha$-stable distributions, $\alpha \in(0,1]$”, Banach Center Publ., 90, 2010, 79–82 | MR | Zbl

[12] Misiewicz J. K., Oleszkiewicz K., Urbanik K., “Classes of measures closed under mixing and convolution. Weak stability”, Studia Math., 167:3 (2005), 195–213 | DOI | MR | Zbl

[13] Misiewicz J. K., “Infinite divisibility of substable processes. II: Logarithm of probability measure”, J. Math. Sci., 81:5 (1996), 2970–2979 | DOI | MR | Zbl

[14] Misiewicz J. K., “Weak stability and generalized weak convolution for random vectors and stochastic processes”, IMS Lecture Notes Monog. Ser., 48, 2006, 109–118 | MR | Zbl

[15] Misiewicz J. K., Mazurkiewicz G., “On $(c,p)$-pseudostable random variables”, J. Theoret. Probab., 18:4 (2005), 837–852 | DOI | MR | Zbl

[16] Oleszkiewicz K., “On $p$-pseudostable random variables, Rosenthal spaces and $\ell_p^n$ ball slicing”, Lecture Notes in Math., 1807, Springer, Berlin, 2003, 188–210 | MR | Zbl

[17] Sato Ken-iti, Lévy Processes and Infinitely Divisible Distributions, Cambridge Univ. Press, Cambridge, 2004 | MR

[18] Schoenberg I. J., “Metric spaces and completely monotonic functions”, Ann. Math., 38 (1938), 811–841 | MR

[19] Urbanik K., “Remarks on $B$-stable probability distributions”, Bull. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 24:9 (1976), 783–787 | MR | Zbl

[20] Urbanik K., “Generalized convolutions”, Studia Math., 23 (1964), 217–245 | MR | Zbl

[21] Urbanik K., “Generalized convolutions, II”, Studia Math., 45 (1973), 57–70 | MR | Zbl

[22] Urbanik K., “Generalized convolutions, III”, Studia Math., 80 (1984), 167–189 | MR | Zbl

[23] Urbanik K., “Generalized convolutions, IV”, Studia Math., 83 (1986), 57–95 | MR | Zbl

[24] Urbanik K., “Quasi-regular generalized convolutions”, Colloquium Math., 55:1 (1988), 147–162 | MR | Zbl

[25] Vol'kovich V., “On symmetric stochastic convolutions”, J. Theoret. Probab., 5:3 (1992), 417–430 | DOI | MR | Zbl

[26] Volkovich V., “O beskonechno razlozhimykh merakh v algebrakh so sluchainoi svertkoi”, Problemy ustoichivosti stokhasticheskikh modelei, VNIISI, M., 1985, 15–24 | MR

[27] Volkovich V., “Mnogomernye B-ustoichivye raspredeleniya i nekotorye obobschennye svertki”, Problemy ustoichivosti stokhasticheskikh modelei, VNIISI, M., 1984, 40–53