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Strong differential subordination and stochastic integration. (English) Zbl 0816.60046

Various sharp inequalities are established connecting the “size” of the stochastic integral \(Y= \int HdX\) and the “size” of a semimartingale integrator \(X\) for bounded predictable integrands \(H\). The proofs are mainly based on adequate choice of special functions related to some boundary value problems.
Reviewer: M.Jerschow (Essen)

MSC:

60H05 Stochastic integrals
60G42 Martingales with discrete parameter
60G46 Martingales and classical analysis
31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions
60E15 Inequalities; stochastic orderings
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