## Bernoulli

• Bernoulli
• Volume 24, Number 4A (2018), 2752-2775.

### Sticky processes, local and true martingales

#### Abstract

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.

#### Article information

Source
Bernoulli, Volume 24, Number 4A (2018), 2752-2775.

Dates
Revised: March 2017
First available in Project Euclid: 26 March 2018

https://projecteuclid.org/euclid.bj/1522051224

Digital Object Identifier
doi:10.3150/17-BEJ944

Mathematical Reviews number (MathSciNet)
MR3779701

Zentralblatt MATH identifier
06853264

#### Citation

Rásonyi, Miklós; Sayit, Hasanjan. Sticky processes, local and true martingales. Bernoulli 24 (2018), no. 4A, 2752--2775. doi:10.3150/17-BEJ944. https://projecteuclid.org/euclid.bj/1522051224

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