Burkholder, Donald L. Strong differential subordination and stochastic integration. (English) Zbl 0816.60046 Ann. Probab. 22, No. 2, 995-1025 (1994). 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) Cited in 5 ReviewsCited in 22 Documents 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 Keywords:inequalities; stochastic integral; predictable integrands; boundary value problems PDFBibTeX XMLCite \textit{D. L. Burkholder}, Ann. Probab. 22, No. 2, 995--1025 (1994; Zbl 0816.60046) Full Text: DOI