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 Electronic Journal of Probability > Vol. 5 (2000) > Paper 1 open journal systems 


Martingales on Random Sets and the Strong Martingale Property

Michael J. Sharpe, University of California, San Diego


Abstract
Let X be a process defined on an optional random set. The paper develops two different conditions on X guaranteeing that it is the restriction of a uniformly integrable martingale. In each case, it is supposed that X is the restriction of some special semimartingale Z with canonical decomposition Z=M+A. The first condition, which is both necessary and sufficient, is an absolute continuity condition on A. Under additional hypotheses, the existence of a martingale extension can be characterized by a strong martingale property of X. Uniqueness of the extension is also considered.


Full text: PDF

Pages: 1-17

Published on: December 16, 1999
Bibliography
  1. Dellacherie, C. and Meyer, P.-A. (1975), Probabilites et Potentiel, 2nd ed; Chapitres I-IV, Hermann, Paris. Math. Review 58:7757
  2. Dellacherie, C. and Meyer, P.-A. (1980), Probabilites et Potentiel, 2nd ed; Chapitres V-VIII, Hermann, Paris. Math. Review 82b:60001
  3. Jeulin, T. (1980), Semi-Martingales et Grossissement d'une Filtration, Lecture Notes in Mathematics 833, Springer, Berlin Heidelberg New York. Math. Review 82h:60106
  4. Maisonneuve, B. (1977) Une mise au point sur les martingales locales definies sur un intervalle stochastique, Lecture Notes in Mathematics 581, Springer, Berlin Heidelberg New York, 435-445. Math. Review 57:14127
  5. Sharpe, M. J. (1988), General Theory of Markov Processes, Academic Press, San Diego. Math. Review 89m:60169
  6. Sharpe, M. J. (1992), Closing values of martingales with finite lifetimes, Seminar on Stochastic Processes 1991, Birkhauser, Boston Basel Berlin, 169-186. Math. Review 93g:60092
  7. Yan, J.-A. (1982), Martingales locales sur un ouvert droit optionnel, Stochastics 8, 161-180. Math. Review 85d:60089
  8. Zheng, W. A. (1982), Semimartingales in predictable random open sets, Lecture Notes in Mathematics 920, Springer, Berlin Heidelberg New York, 370-379. Math. Review 83k:60052
















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Electronic Journal of Probability. ISSN: 1083-6489