Advanced topics of stochastic processes

Advanced topics of stochastic processes

1. Stochastic differential equations and Ito calculus

2. Power spectrum

3. Multivariate Ornstein-Uhlenbeck process

4. Feynman Kac-formula

5. Kramers-Moyal expansion, van Kampen size expansion

6. Non commuting random variables: Random matrices

7. Interacting particle models: the Voter Model

 

 

Bibliography

Van Kampen, Nicolaas Godfried. Stochastic processes in physics and chemistry. Vol. 1. Elsevier, 1992.

Gardiner, Crispin W. Handbook of stochastic methods. IV ed. springer, 2014.

Kuo, H. H. "Introduction to Stochastic Integration. 2006.

Tu, Chengyi, et al. "Cooperation promotes biodiversity and stability in a model ecosystem." arXiv preprint arXiv:1708.03154 (2017).

Allesina, Stefano, and Si Tang. "The stability–complexity relationship at age 40: a random matrix perspective." Population Ecology 57.1 (2015): 63-75.