Sharp maximal inequalities for stochastic integrals in which the integrator is a submartingale

Hammack, William

doi:10.1090/S0002-9939-96-03225-X

Sharp maximal inequalities for stochastic integrals in which the integrator is a submartingale
HTML articles powered by AMS MathViewer

by William Hammack PDF

Proc. Amer. Math. Soc. 124 (1996), 931-938 Request permission

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

Klaus Bichteler, Stochastic integration and $L^{p}$-theory of semimartingales, Ann. Probab. 9 (1981), no. 1, 49–89. MR 606798
D. L. Burkholder, Boundary value problems and sharp inequalities for martingale transforms, Ann. Probab. 12 (1984), no. 3, 647–702. MR 744226
Donald L. Burkholder, Sharp inequalities for martingales and stochastic integrals, Astérisque 157-158 (1988), 75–94. Colloque Paul Lévy sur les Processus Stochastiques (Palaiseau, 1987). MR 976214
Donald L. Burkholder, Differential subordination of harmonic functions and martingales, Harmonic analysis and partial differential equations (El Escorial, 1987) Lecture Notes in Math., vol. 1384, Springer, Berlin, 1989, pp. 1–23. MR 1013814, DOI 10.1007/BFb0086792
—, Strong differential subordination and stochastic integration, Ann. Probab. 22 (1994), 995–1025.
Claude Dellacherie and Paul-André Meyer, Probabilities and potential. B, North-Holland Mathematics Studies, vol. 72, North-Holland Publishing Co., Amsterdam, 1982. Theory of martingales; Translated from the French by J. P. Wilson. MR 745449
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.