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2013 Optimal Novikov-type criteria for local martingales with jumps
Alexander Sokol
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Electron. Commun. Probab. 18: 1-8 (2013). DOI: 10.1214/ECP.v18-2312


We consider cadlag local martingales M with initial value zero and jumps larger than a for some a larger than or equal to -1, and prove Novikov-type criteria for an exponential local martingale to be a uniformly integrable martingale. We obtain criteria using both the quadratic variation and the predictable quadratic variation. We prove optimality of the coefficients in the criteria. As a corollary, we obtain a verbatim extension of the classical Novikov criterion for continuous local martingales to the case of local martingales with initial value zero and nonnegative jumps.


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Alexander Sokol. "Optimal Novikov-type criteria for local martingales with jumps." Electron. Commun. Probab. 18 1 - 8, 2013.


Accepted: 23 May 2013; Published: 2013
First available in Project Euclid: 7 June 2016

zbMATH: 1312.60051
MathSciNet: MR3064998
Digital Object Identifier: 10.1214/ECP.v18-2312

Primary: 60G44

Keywords: exponential martingale , martingale , Novikov , optimal , Poisson process , uniform integrability

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