ON Φ-INEQUALITIES FOR BOUNDED SUBMARTINGALES AND SUBHARMONIC FUNCTIONS
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Let f = (fn) be a nonnegative submartingale such that [수식] and g = (gn) be a martingale, adapted to the same filtration, satisfying [수식] The paper contains the proof of the sharp inequality [수식] for a class of convex increasing functions Φ on [0, ∞), satisfying certain growth condition. As an application, we show a continuous-time version for stochastic integrals and a related estimate for smooth functions on Euclidean domain.
Abstract
Let f = (fn) be a nonnegative submartingale such that [수식] and g = (gn) be a martingale, adapted to the same filtration, satisfying [수식] The paper contains the proof of the sharp inequality [수식] for a class of convex increasing functions Φ on [0, ∞), satisfying certain growth condition. As an application, we show a continuous-time version for stochastic integrals and a related estimate for smooth functions on Euclidean domain.
참고문헌 (5)
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- D. L. Burkholder, "Explorations in martingale theory and its applications, ´Ecole d’Ete de Probabilit ´es de Saint-Flour XIX—1989", pp.1~66 (1991), Springer
- D. L. Burkholder, "Strong differential subordination and stochastic integration", Ann. Probab, 22, pp.995~1025 (1994)
- Y.-H. Kim, "A submartingale inequality", Commun. Korean Math. Soc, 13(1), pp.159~170 (1998)