Reading List
MATH 6962-1, Spring 2004


Reading List has been updated to include material assigned on

April 15, 2004

All readings will be listed here, organized by topic. Dates indicate the class by which you should have read the indicated material.   Some readings may be announced here before they are announced in class, in case you want to read ahead.   Sometimes, particularly if I am traveling, you may find some references posted at the library class reserves before they are linked here.
If a reading does not have a date, you don't have to worry about it yet.


Fundamentals of Probability Theory and Stochastic Processes

Assigned Readings

Finite-State, Discrete-Time Markov Chains

Assigned Readings

  • Lawler, Intoduction to Stochastic Processes, Ch. 1 (PDF) (03/08/04)
  • Optional Readings

    Countable State, Discrete-Time Markov Chains

    Assigned Readings

  • Lawler, Intoduction to Stochastic Processes, Ch. 2 (PDF) (03/25/04)
  • Karlin & Taylor, A First Course in Stochastic Processes, Ch. 2 and 3 (PDF) (03/22/04)
  • Countable State, Continuous-Time Markov Chains

    Assigned Readings

  • Lawler, Intoduction to Stochastic Processes, Ch. 3 (PDF)  (04/01/04)
  • Andersson and Britton, Stochastic Epidemic Models and Their Statistical Analysis, Ch. 2 (PDF) (04/12/04)
  • Optional Readings

    Martingales

    Assigned Readings

  • Karlin & Taylor, A First Course in Stochastic Processes, Sec. 6.1-6.4 (PDF) (04/12/04)
  • Continuous Space, Continuous-Time Markov Processes

    Assigned Readings

  • Kloeden and Platen, Numerical Solution of Stochastic Differential Equations, Sec. 1.7,1.8 (PDF) (04/19/04)
  • Kloeden and Platen, Numerical Solution of Stochastic Differential Equations, Sec. 2.3,2.4 (PDF) (04/22/04)
  • Optional Readings

  • Friedman, Stochastic Differential Equations and Applications, Ch. 2
  •  

    Stochastic Calculus

    Assigned Readings

  • Kloeden and Platen, Numerical Solution of Stochastic Differential Equations, Ch. 3 (PDF) (04/30/04)
  •  

    Stochastic Differential Equations

    Optional Readings

  • Kloeden and Platen, Numerical Solution of Stochastic Differential Equations, Ch. 4.1, 4.5, 4.6, 4.8, 4.9 (PDF)
  • Kloeden and Platen, Numerical Solution of Stochastic Differential Equations, Ch. 6.1, 6.3  (PDF)
  • Numerical Solution of Stochastic Differential Equations

    Assigned Readings

  • Higham, "An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations," SIAM Review 43 (3),  525-546 (2001)
  • Financial Derivatives and Partial Differential Equations

    Optional Readings
  • Almgren, "Financial Derivatives and Partial Differential Equations," American Mathematical Monthly 109 (1),  1-12 (2002)