Numerical Integration of Stochastic Differential Equations


In this course we will introduce and study numerical integrators for stochastic differential equations. These numerical methods are important for many applications.

Mean-square  (dark gray) and asymptotic stability region (dark and light grays) of the explicit Milstein–Talay method.

Sample of an SPDE modelling the electric potential in a neuron at fixed time (left), as a space-time function (right).


Dr. Adrian Blumenthal


Giacomo Garegnani will be present in his office, MA C2 614, on Monday from 15:15 to 16:15 to answer your questions.

Organization of the course

Course: Tuesday from 16:15 to 18:00 at MA A3 31
Exercise session: Monday from 13:15 to 15:00 at MA A1 12


Some notions and notations of probability theory needed in the course: 

Mini project

The mini project is optional and is due Sunday 16 June 2019. Detailed information:


Week Series Week Series Week Series
Series 1
Series 2
Series 3
Series 4
Series 5
Series 6
Series 7
Series 8
Series 9
Series 10
Series 11
Series 12
Series 13



L. Arnold, “Stochastic Differential Equations, Theory and applications”.

L.C. Evans, “An Introduction to Stochastic Differential Equations”, AMS, 2013.

A. Einstein, “Investigations on the theory of the Brownian Movement”, Dover Publications, INC., 1956. 

D. Talay, “Discrétisation d’une équation différentielle stochastique et calcul approché d’espérances de fonctionnelles de la solution”, Modélisation mathématique et analyse numérique, 1986. 

H-H. Kuo, “Introduction to Stochastic Integration”, Springer, 2005.

P.E. Kloeden, E. Platen, “Numerical Solution of Stochastic Differential Equations”, second edition, Springer, 1999.

G.N. Milstein, M.V. Tretyakov, “Stochastic Numerics for Mathematical Physics”, Springer, 2004.


References for bases of probability theory:

R. C. Dalang et D. Conus, “Introduction à la théorie des probabilités”, 1ère édition, PPUR, 2014

R. Derrett, “Probability: Theory and Examples“, Cambridge University Press 2010.

A. Gut, “Probability: A Graduate Course”, 2nd édition, Springer, 2013.

Ch.E. Pfister, “Théorie des probabilités”, première édition, PPUR, 2014.

J. Jacod, P. Protter, “Probability essentials”, 2nd edition, Springer, 2004.