Stochastic methods in physics and biology, spring 2016
Stochastic methods in physics and biology, spring 2016
Teacher: Paolo Muratore-Ginanneschi
Teaching Assistant: Joonas Turunen
Scope: 10 cr
Type: Advanced studies
Teaching:
Topics:
Prerequisites:
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News
- No lecture on Fri 04.03 and on Fri 01.01. We will agree on the dates for making up for these lectures.
Teaching schedule
Weeks 3-9 and 11-18, Monday and Friday 14-16 in room B120.
First lecture Friday 22.01
Easter holiday 24.-30.3.
Exams
Written test of 2h and 30 min maximal duration to be held in a date to be agreed after the end of the course
First exam call: FRIDAY 13.05 from 11:00 to 15:00 in either A111 or B123.
Course material
The main reference for the course, besides lecture notes, is
- Pavliotis, Grigorios A. Stochastic processes and applications : diffusion processes, the Fokker-Planck and Langevin equations, Springer 2014
(e-reading available from the Helsinki University Library)
Lecture notes
Lectures 1-10 | Lectures 10-20 |
|---|---|
: Kolmogorov axioms (set - event correspondence ) | : Some exactly solvable stochastic differential equations |
: On independence, conditional probability and Bayes' formula | : PDE's and martingales |
: Stochastic processes, stationarity and a.s. convergence | : Dynkin's and Feynman-Kac formulas |
: Stationarity and ergodicity | : Diffusions in domains with boundaries |
: Wiener process and Markov processes | : Langevin's equation |
: Kolmogorov's equations | Lecture 16: A succint overview of Smoluchowski equation |
: Ito calculus without probability | : Statistics of exit times from a domain |
: Stochastic integrals | : One dimensional diffusions |
: Stochastic differential equations | : Feller's analysis of boundary conditions for 1d diffusions |
A martingale intermezzo | Lecture 20: Numerical methods |
Presemo
The course as a dedicated presemo room (web space). To access this web space just follow the foregoing link. Students are encouraged to use the presemo room for any civilized activity pertaining the course. We will also try to use the presemo room during the lectures for checking the student response to multi-answer questions. For this reason, we encourage students to have a mobile device with them when attending classes.
Registration
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Exercises
Exercise sessions on Fridays 12-14 in B321, starting from 29.1.2016. Extra points for the exam from solved exercises: 25%-> 1p, 50%-> 2p, 75%-> 3p. One additional point after participating in at least 80% of the exercise sessions.
Assignments
Exercise classes
Group | Day | Time | Room | Instructor |
|---|---|---|---|---|
1. | Fri | 12-14 | B321 | Joonas Turunen |
Bibliography
The following list comprises some extra references which I found useful while preparing course material.
Gardiner C. W., "Handbook of stochastic methods for physics, chemistry and the natural sciences" (Springer), 1994, 13, 442.
- Nelson E. "Dynamical Theories of Brownian Motion" Princeton University Press 1967 (freely available)
Evans L. C., "An Introduction to Stochastic Differential Equations", Berkeley lecture notes.
van Handel R., "Stochastic Calculus, Filtering, and Stochastic Control", CalTech lecture notes (2007).
Klebaner F. C., "Introduction to stochastic calculus with applications" (Imperial College Press), 2005, 416.
Higham D. J., "An algorithmic introduction to numerical simulation of stochastic differential equations", SIAM Review, Education Section, 43, 2001, 525-546.
- Boffetta G., Vulpiani A. "La Probabilità in Fisica" (in italian) Springer, 2012, 236
Durrett R., "Essentials of Stochastic Processes" Springer, 2012, 265
Durrett R., "Probability models for DNA sequence evolution", Springer 2008, 432 (e-reading from UH)
Steele, J. M., "Stochastic calculus and financial applications", Springer, 2001, 300.
Course feedback
Course feedback can be given at any point during the course. Click here.