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 Electronic Communications in Probability > Vol. 13 (2008) > Paper 61 open journal systems 


Sharp inequality for bounded submartingales and their differential subordinates

Adam Osekowski, University of Warsaw


Abstract
Let α be a fixed number from the interval [0,1]. We obtain the sharp probability bounds for the maximal function of the process which is α-differentially subordinate to a bounded submartingale. This generalizes the previous results of Burkholder and Hammack.


Full text: PDF

Pages: 660-675

Published on: December 19, 2008
Bibliography
  1. D. L. Burkholder. Explorations in martingale theory and its applications. Ecole d'Ete de Probabilités de Saint-Flour XIX---1989, 1--66, Lecture Notes in Math., 1464, Springer, Berlin, 1991. Math. Review 92m:60037
  2. D. L. Burkholder. Strong differential subordination and stochastic integration. Ann. Probab. 22 (1994), 995-1025. Math. Review 95h:60085
  3. C. Choi. A submartingale inequality. Proc. Amer. Math. Soc. 124 (1996), 2549-2553. Math. Review 96j:60083
  4. W. Hammack. Sharp inequalities for the distribution of a stochastic integral in which the integrator is a bounded submartingale. Ann. Probab. 23 (1995), 223-235. Math. Review 96g:60056
















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Electronic Communications in Probability. ISSN: 1083-589X