Strong Differential Subordination and Stochastic Integration

Part of the Selected Works in Probability and Statistics book series (SWPS)


How does the size of a stochastic integral vary with the choice of the predictable integrand and the semimartingale integrator? One of our goals here is to throw new light on this question, especially in the case that the integrator is not necessarily a martingale but belongs to some other class of semimartingales.


Strict Inequality Harmonic Measure Predictable Process Closed Unit Ball Maximal Inequality 


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  1. 1.
    BICHTELER, K. (1981). Stochastic integration and L p-theory of semimartingales. Ann. Probab. 949-89.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    BURKHOLDER D. L. (1984). Boundary value problems and sharp inequalities for martingale transforms. Ann. Probab. 12647-702.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    BurkholderD. L. (1986). Martingales and Fourier analysis in Banach spaces. Probability and Analysis. Lecture Notes in Math. 120661-108. Springer, Berlin.CrossRefMathSciNetGoogle Scholar
  4. 4.
    BurkholderD. L. (1987). A sharp and strict L p-inequality for stochastic integrals. Ann. Probab. 15268-273.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    BurkholderD. L. (1988). Sharp inequalities for martingales and stochastic integrals. Colloque Paul Levy sur les processus stochastiques. Astérisque 157-15875-94.MathSciNetGoogle Scholar
  6. 6.
    BurkholderD. L. (1989). Differential subordination of harmonic functions and martingales. Harmonic Analysis and Partial Differential Equations. Lecture Notes in Math. 1384 1-23. Springer, Berlin.Google Scholar
  7. 7.
    BurkholderD. L. (1989). On the number of escapes of a martingale and its geometrical significance. In Almost Everywhere Convergence(G. A. Edgar and L. Sucheston, eds.) 159-178. Academic, New York.Google Scholar
  8. 8.
    BurkholderD. L. (1991). Explorations in martingale theory and its applications. Ecole d’Eté de Probabilités de Saint-Flour XIX. Lecture Notes in Math. 14641-66. Springer, Berlin.CrossRefMathSciNetGoogle Scholar
  9. 9.
    BurkholderD. L. (1993). Sharp probability bounds for Itô processes. In Current Issues in Statistics and Probability: Essays in Honor of Raghu Raj Bahadur(J. K. Ghosh, S. K. Mitra, K. R. Parthasarathy and B. L. S. Prakasa Rao, eds.) 135-145. Wiley Eastern, New Delhi.Google Scholar
  10. 10.
    DellacherieC. and MeyerP. A. (1980). Probabilités et Potentiel: Théorie des Martingales. Hermann, Paris.MATHGoogle Scholar
  11. 11.
    EdwardsD. A. (1990). A note on stochastic integrators. Math. Proc. Cambridge Philos. Soc. 107395-400.MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    IkedaN. and WatanabeS. (1981). Stochastic Differential Equations and Diffusion Processes. North-Holland, Amsterdam.MATHGoogle Scholar

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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Mathematics and Department of StatisticsPurdue UniversityWest LafayetteUSA
  2. 2.Department of MathematicsUniversity of IllinoisUrbanaUSA

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