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

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 |