The problem sets were due in the lectures noted in the table. 40% of the grade is based on the problem sets.
Assignments table.
| LEC # |
ASSIGNMENTS |
SOLUTIONS |
| 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.
| LEC # |
ASSIGNMENTS |
TOPICS |
| 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
|