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November 2018 Sticky processes, local and true martingales
Miklós Rásonyi, Hasanjan Sayit
Bernoulli 24(4A): 2752-2775 (November 2018). DOI: 10.3150/17-BEJ944


We prove that for a so-called sticky process $S$ there exists an equivalent probability $Q$ and a $Q$-martingale $\tilde{S}$ that is arbitrarily close to $S$ in $L^{p}(Q)$ norm. For continuous $S$, $\tilde{S}$ can be chosen arbitrarily close to $S$ in supremum norm. In the case where $S$ is a local martingale we may choose $Q$ arbitrarily close to the original probability in the total variation norm. We provide examples to illustrate the power of our results and present an application in mathematical finance.


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Miklós Rásonyi. Hasanjan Sayit. "Sticky processes, local and true martingales." Bernoulli 24 (4A) 2752 - 2775, November 2018.


Received: 1 September 2015; Revised: 1 March 2017; Published: November 2018
First available in Project Euclid: 26 March 2018

zbMATH: 06853264
MathSciNet: MR3779701
Digital Object Identifier: 10.3150/17-BEJ944

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability


Vol.24 • No. 4A • November 2018
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