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Sharp maximal inequalities for stochastic integrals in which the integrator is a submartingale
Author(s):
William
Hammack
Journal:
Proc. Amer. Math. Soc.
124
(1996),
931-938.
MSC (1991):
Primary 60G42, 60H05;
Secondary 60E15
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Abstract:
We obtain sharp maximal inequalities for strong subordinates of real-valued submartingales. Analogous inequalities also hold for stochastic integrals in which the integrator is a submartingale. The impossibility of general moment inequalities is also demonstrated.
References:
- 1.
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 -theory of semimartingales, Ann. Probab. 9 (1981), 49--89. MR 82g:60071 - 2.
- D. L. Burkholder, Boundary value problems and sharp inequalities for martingale transforms, Ann. Probab. 12 (1984), 647--702. MR 86b:60080
- 3.
- ------, Sharp inequalities for martingales and stochastic integrals, Astérisque 157 (1988), 75--94. MR 90b:60051
- 4.
- ------, Differential subordination of harmonic functions and martingales, Proceedings of the Seminar on Harmonic Analysis and Partial Differential Equations, El Escorial, 1987, Lecture Notes in Math., vol. 1384, Springer-Verlag, New York, 1989, pp. 1--23. MR 90k:31004
- 5.
- ------, Strong differential subordination and stochastic integration, Ann. Probab. 22 (1994), 995--1025. CMP 94:16
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- C. Dellacherie and P. Meyer, Probabilities and potentials B, North-Holland, Amsterdam, 1982. MR 85e:60001
- 7.
- 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.
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Additional Information:
William
Hammack
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z2
Email:
hammack@math.ubc.ca
DOI:
10.1090/S0002-9939-96-03225-X
PII:
S 0002-9939(96)03225-X
Keywords:
Martingale,
submartingale,
maximal inequality,
differential subordination,
strong subordination,
stochastic integral
Received by editor(s):
June 15, 1994
Received by editor(s) in revised form:
September 20, 1994
Communicated by:
Richard T. Durrett
Copyright of article:
Copyright
1996,
American Mathematical Society
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