Geodesic
A contribution to the theory of asymptotic martingales
Glasgow mathematical journal, Tome 23 (1982) no. 2, pp. 177-186

Voir la notice de l'article provenant de la source Cambridge University Press

During the last few years several articles on asymptotic martingales (amarts) have appeared. The first unified treatment was given by Edgar and Sucheston in [7], where further references can be found. The purpose of this paper is to add some further results to the theory of amarts. 
Gut, Allan. A contribution to the theory of asymptotic martingales. Glasgow mathematical journal, Tome 23 (1982) no. 2, pp. 177-186. doi: 10.1017/S001708950000495X
@article{10_1017_S001708950000495X,
     author = {Gut, Allan},
     title = {A contribution to the theory of asymptotic martingales},
     journal = {Glasgow mathematical journal},
     pages = {177--186},
     year = {1982},
     volume = {23},
     number = {2},
     doi = {10.1017/S001708950000495X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708950000495X/}
}
TY  - JOUR
AU  - Gut, Allan
TI  - A contribution to the theory of asymptotic martingales
JO  - Glasgow mathematical journal
PY  - 1982
SP  - 177
EP  - 186
VL  - 23
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S001708950000495X/
DO  - 10.1017/S001708950000495X
ID  - 10_1017_S001708950000495X
ER  - 
%0 Journal Article
%A Gut, Allan
%T A contribution to the theory of asymptotic martingales
%J Glasgow mathematical journal
%D 1982
%P 177-186
%V 23
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S001708950000495X/
%R 10.1017/S001708950000495X
%F 10_1017_S001708950000495X

[1] 1.Austin, D. G., Edgar, G. A., and Tulcea, A. Ionescu, Pointwise convergence in terms of expectations, Z. Wahrsch. Verw. Gebiete 30 (1974), 17–26. Google Scholar | DOI

[2] 2.Baxter, J. R., Pointwise in terms of weak convergence, Proc. Amer. Math. Soc. 46 (1974), 395–398. Google Scholar | DOI

[3] 3.Bellow, A., Stability properties of the class of asymptotic martingales, Bull. Amer. Math. Soc. 82 (1976), 338–340. Google Scholar | DOI

[4] 4.Bellow, A., Several stability properties of the class of asymptotic martingales, Z. Wahrsch. Verw. Gebiete 37 (1977), 275–290. Google Scholar | DOI

[5] 5.Blackwell, D. and Dubins, L. E., A converse to the dominated convergence theorem, Illinois J. Math. 7 (1963), 508–514. Google Scholar | DOI

[6] 6.Doob, J. L., Stochastic processes (Wiley, 1953). Google Scholar

[7] 7.Edgar, G. A. and Sucheston, L., Amarts: A class of asymptotic martingales. A. Discrete parameter, J. Multivariate Anal. 6 (1976), 193–221. Google Scholar | DOI

[8] 8.Gut, A., Moments of the maximum of normed partial sums of random variables with multidimensional indices, Z. Wahrsch. Verw. Gebiete 46 (1979), 205–220. Google Scholar | DOI

[9] 9.Klass, M. J., On stopping rules and the expected supremum of S /a and |S|/ a, Ann. Probab. 2 (1974), 889–905. Google Scholar | DOI

[10] 10.Krengel, U. and Sucheston, L., On semiamarts, amarts and processes with finite value, Advances in Probability 4 (1978), 197–266. Google Scholar

[11] 11.Loève, M., Probability theory, 3rd edition (Van Nostrand, 1963). Google Scholar

[12] 12.Mertens, J. F., Théorie des processus stochastiques genéraux applications aux surmartingales, Z. Wahrsch. Verw. Gebiete 22 (1972), 45–68. Google Scholar | DOI

[13] 13.Meyer, P. A., Probabilityés et Potentiel (Hermann, 1966). Google Scholar

[14] 14.Neveu, J., Discrete-parameter martingales (North-Holland, 1975). Google Scholar

[15] 15.Sudderth, W., A “Fatou equation” for randomly stopped variables, Ann. Math. Statist. 42 (1971), 2143–2146. Google Scholar | DOI

Cité par Sources :