A Criterion for Tightness for a Sequence of Martingales
Loynes, R. M.
Ann. Probab., Tome 4 (1976) no. 6, p. 859-862 / Harvested from Project Euclid
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An improved result is presented, showing that if the finite-dimensional distributions of a sequence of martingales converge, and if for each time $t$ the variables are uniformly integrable, then weak convergence follows (in either $C$ or $D$) provided the limiting process satisfies a certain condition; this condition is satisfied by the Wiener process.
Publié le : 1976-10-14
Classification:  Martingales,  weak convergence,  tightness,  60B10,  60F05,  60G45 
@article{1176995990,
     author = {Loynes, R. M.},
     title = {A Criterion for Tightness for a Sequence of Martingales},
     journal = {Ann. Probab.},
     volume = {4},
     number = {6},
     year = {1976},
     pages = { 859-862},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176995990}
}

Loynes, R. M. A Criterion for Tightness for a Sequence of Martingales. Ann. Probab., Tome 4 (1976) no. 6, pp.  859-862. http://gdmltest.u-ga.fr/item/1176995990/