Strong Differential Subordination and Stochastic Integration
Donald L. Burkholder · The Annals of Probability · 1994
This paper contains sharp norm, maximal, escape and exponential inequalities for stochastic integrals in which the integrator is either a nonnegative submartingale or a nonnegative supermartingale. Analogous inequalities hold for Ito processes and for smooth functions on Euclidean domains.