Stochastic methods in physics and biology, spring 2016


Teacher: Paolo Muratore-Ginanneschi 

Teaching Assistant: Joonas Turunen

Scope: 10 cr

Type: Advanced studies






  •  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.  


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

Lecture notes

Lectures 1-10Lectures 10-20
Lecture 01: Kolmogorov axioms (set - event correspondence table ) Lecture 11 :  Some exactly solvable stochastic differential equations
Lecture 02: On independence, conditional probability and Bayes' formulaLecture 12 : PDE's and martingales
Lecture 03: Stochastic processes, stationarity and a.s. convergence Lecture 13 : Dynkin's and Feynman-Kac formulas
Lecture 04 : Stationarity and ergodicityLecture 14: Diffusions in domains with boundaries
Lecture 05: Wiener process and Markov processes Lecture 15 : Langevin's equation
Lecture 06: Kolmogorov's equationsLecture 16: A succint overview of Smoluchowski equation
Lecture 07: Ito calculus without probabilityLecture 17: Statistics of exit times from a domain
Lecture 08: Stochastic integralsLecture 18: One dimensional diffusions
Lecture 09: Stochastic differential equationsLecture 19: Feller's analysis of boundary conditions for 1d diffusions
Lecture 10: A martingale intermezzoLecture 20: Numerical methods


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.



Did you forget to register?   What to do?


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.




  • Exercise classes

1.Fri12-14B321Joonas Turunen
  • Bibliography

The following list comprises some extra references which I found useful while preparing course material.

Course feedback can be given at any point during the course. Click here.



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