Stochastic methods in physics and biology, spring 2014
Stochastic methods in physics and biology, spring 2014
Lecturer
Matteo Marcozzi (assistant)
Scope
10 sp.
The aim of the course is to introduce the basic concepts of the theory of stochastic differential equations needed in applications (applied mathematics, physics and biology).
Prerequisites
Type
Advanced studies
Prerequisites
The course is intended for undergraduate students of mathematics, physics. Prior courses in advanced calculus and linear algebra are required (Diff.Int. 12 and Lineaarialgebra 1, or Mapu 12).
Lectures
Weeks 49 and 1118, Monday 1416 in room D123, and Friday 1416 in room C123.
Easter holiday 17.23.4.
Lecture Notes
The lecture notes cover and sometimes integrate the material expounded in the lections. They also give bibliographic references for the same topics.
Lectures 110  Lectures 1020 

: Probability spaces and random variables (v 11.02)  : Karhunen–Loève representation of the Brownian motion 
Independence, conditional expectations and inequalities (v 11.02)  : Calculus for paths of finite quadratic variation (v 04.04) 
: Classical limit theorems (v 11.02)  : Ito integrals (v. 08.04) 
: Sequences of random variables and martingales (v 07.02)  : Stratonovich integral, stochastic differential equations (v 08.04) 
: From Bernoulli variables to Random Walk (v 11.02) 

: Continuous Time Random Walks and MontrollWeiss equation 

: Asymptotic analysis of the Montroll–Weiss process 

: Girsanov formula for continuous Markov Processes 

: Kolmogorov axioms and Kolmogorov–Chentsov theorem (v. 21.03) 

: Brownian motion (v. 21.03) 

Exams
Bibliography
 Schuss Z., "Theory and Applications of Stochastic Processes: An Analytical Approach" (Springer), 2010, 170, 468.
Gardiner C. W., "Handbook of stochastic methods for physics, chemistry and the natural sciences" (Springer), 1994, 13, 442.
Evans L. C., "An Introduction to Stochastic Differential Equations", Berkeley lecture notes.
van Handel R., "Stochastic Calculus 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, 525546. (Link to Higham's publications page.)
Registration
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Exercise session
Group  Day  Time  Place  Lecturer 

1.  Friday  1618  B321 
Exercise Notes 


Notes 01 

Notes 02 

Exercise Session 

Exercise Session 08 










