Abstract
We prove a stochastic Gronwall lemma of the convolution type. Our results extend that of Scheutzow [A stochastic Gronwall lemma, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 16 (2013) 1350019], and the related results established in the non-convolution case. The proofs of the present results are essentially based on the Métivier–Pellaumail inequality for semimartingales.
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