Probability III: Continuous time processes

Summary

This course extends the concepts exposed in Probability II into the world of continuous time. We explore martingales and Markov processes, guided by the core examples of Brownian Motion and Poisson Processes. A particular emphasis is placed on Brownian Motion, with its innumerable applications.

Content

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Learning Prerequisites

Required courses

Second year mandatory courses, Probability II

Recommended courses

Measure theory

Teaching methods

Weekly lectures and problem classes

Assessment methods

Written examination in the summer session

Supervision

Office hours	No
Assistant.e.s	Yes
Forum	Yes

Resources

Bibliography

This course is designed to be self-contained within the provided lecture notes. However, to consolidate the material and for further reading, the following references may be of use:

- Karatzas, I. and Shreve, S., 2014. Brownian Motion and Stochastic Calculus. Springer.

- Le Gall, J.F., 2016. Brownian Motion, Martingales, and Stochastic Calculus. Springer.

- Revuz, D. and Yor, M., 2013. Continuous Martingales and Brownian Motion. Springer.

- Ethier, S.N. and Kurtz, T.G., 2009. Markov Processes: Characterization and Convergence. John Wiley & Sons.

- Last, G. and Penrose, M., 2018. Lectures on the Poisson Process. Cambridge University Press.

 

Notes/Handbook

Notes will be made available in due course.

Moodle Link

• https://go.epfl.ch/MATH-354