The problem sets were due in the lectures noted in the table. 40% of the grade is based on the problem sets.

5 Problem Set 1 (PDF) (PDF)
8 Problem Set 2 (PDF) (PDF)
14 Problem Set 3 (PDF) (PDF)
18 Problem Set 4 (PDF) (PDF)
25 Problem Set 5 (PDF) (PDF)

The following assignments are from the Spring 2005 version of the course.

4 Problem Set 1 (PDF)

Asymptotics of Rayleigh’s Random Walk, Central Limit Theorem, Gram-Charlier Expansion

Exact Solution for the Position of Cauchy’s Random Walk with Non-identical Steps

Computer Simulation of Pearson’s Random Walk to find the Fraction of Time Spent in the Right Half Plane (“Arcsine Law”) and the First Quadrant

8 Problem Set 2 (PDF)

Percentile Order Statistics, Asymptotics of the Median Versus the Mean

Computer Simulation of the Winding Angle for Pearson’s Random Walk, Logarithmic Scaling and Limiting Distribution

Globally-valid Saddle-point Asymptotics for a Random Walk with Exponentially Distributed Displacements

The Void Model for Granular Drainage, Continuum Limits for the Void Density (Mean Flow Profile) and the Position a Tracer Particle, Exact Similarity Solutions for Parabolic Flow to a Point Orifice

15 Problem Set 3 (PDF)

Modified Kramers-Moyall Expansion for a General Discrete Markov Process

Black-Scholes Formula for a Call Option, Interpretation as Risk Neutral Valuation, Put-call Parity

Continuum Limit of Bouchaud-Sornette Theory for Options with Residual Risk (Corrections to the Black-Scholes Equation)

24 Problem Set 4 (PDF)

Linear Polymer Structure, Random Walk with Exponentially Decaying Correlations, Depending on Temperature

Polymer Surface Adsorption, First Passage to a Plane, Levy Flight for Adsorption Sites, Scalings with the Chain Length

Solution to the Telegrapher’s Equation, Fourier-Laplace Transform, Wave and Diffusion Limits, Exact Green Function

Inelastic Diffusion, Random Walk with Exponentially Decaying Steps, Approach to the Central Limit Theorem

Course Info

Learning Resource Types

assignment_turned_in Problem Sets with Solutions
grading Exams with Solutions
notes Lecture Notes