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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 29, Fasc. 1,
pages 29 - 42
 

SHARP NORM INEQUALITIES FOR STOCHASTIC INTEGRALS IN WHICH THE INTEGRATOR IS A NONNEGATIVE SUPERMARTINGALE

Adam Osękowski

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, 31B05.

Keywords and phrases: Stochastic integral, martingale, supermartingale, norm inequality, differential subordination, conditional differential subordination, superharmonic function, boundary value problem.

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