Abstract
Let , and let , be Itō processes
such that , , and . The purpose of the paper is to determine the optimal universal constant in the weak-type estimate
Then the inequality is extended, with unchanged constant, to the more general setting when is a submartingale and is -strongly differentially subordinate to . As an application, a related estimate for subharmonic functions is established. The inequalities generalize and unify the earlier results of Burkholder, Choi, and Hammack for Itō processes, stochastic integrals, and smooth functions on Euclidean domains.
Citation
Adam Osȩkowski. "A sharp weak-type bound for Itō processes and subharmonic functions." Kyoto J. Math. 51 (4) 875 - 890, Winter 2011. https://doi.org/10.1215/21562261-1424893
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