SHARP NORM INEQUALITIES FOR STOCHASTIC INTEGRALS IN
WHICH THE INTEGRATOR IS A NONNEGATIVE SUPERMARTINGALE
Abstract: The paper is devoted to sharp inequalities between moments of nonnegative
supermartingales and their strong subordinates. Analogous estimates hold true for
stochastic integrals with respect to a nonnegative right-continuous supermartingale.
Similar inequalities are established for smooth functions on Euclidean domains.
2000 AMS Mathematics Subject Classification: Primary: 60G42; Secondary: 60H05,
Keywords and phrases: Stochastic integral, martingale, supermartingale, norm
inequality, differential subordination, conditional differential subordination, superharmonic
function, boundary value problem.