# Change of probability measure for a stochastic process

August 5, 2015 — August 16, 2016

density

measure

probability

time series

🏗 A placeholder for notes on a.e. continuous monotonic changes of measure in order to render a process “simple” in some sense. Something something Martingale something blah blah stochastic calculus.

For a modern, pragmatic application see, e.g. reparamaterisation, or even better neural diffusion.

## 1 References

Applebaum. 2009.

*Lévy Processes and Stochastic Calculus*. Cambridge Studies in Advanced Mathematics 116.
Barndorff-Nielsen, and Shiryaev. 2010.

*Change of Time and Change of Measure*. Advanced Series on Statistical Science & Applied Probability.
Borovkov, and Burq. 2001. “Kendall’s Identity for the First Crossing Time Revisited.”

*Electronic Communications in Probability*.
Burgess. 2014. “Martingale Measures & Change of Measure Explained.” SSRN Scholarly Paper ID 2961006.

Ranneby. 1984. “The Maximum Spacing Method. An Estimation Method Related to the Maximum Likelihood Method.”

*Scandinavian Journal of Statistics*.
Ranneby, Rao Jammalamadaka, and Teterukovskiy. 2005. “The Maximum Spacing Estimation for Multivariate Observations.”

*Journal of Statistical Planning and Inference*, IISA 2002 DeKalb Conference,.
Surace, and Pfister. 2016. “Online Maximum Likelihood Estimation of the Parameters of Partially Observed Diffusion Processes.” In.

Wong, and Li. 2006. “A Note on the Estimation of Extreme Value Distributions Using Maximum Product of Spacings.” In

*Institute of Mathematical Statistics Lecture Notes - Monograph Series*.