Stochastic calculus, Fall 2011

Course Details and Syllabus

Homework, workload, and testing

There will be weekly homework assignments, each due at the beginning of class the following week. Late homework may be accepted at the discression of the instructor, but there will be a lateness penalty. Homework will involve mathematical analysis and small scale computing of various kinds. The each homework assignment is designed to take 10 hours or less. Please let the instructor know if your are spending significantly more time than this. The final exam is the only testing.

Source materials

See the Resources page.


The final grade will be determined by the grades on the homework assignments and the final exam, each counting for about half the total. Homework grades will be posted on the nyuHome web site. Only registered students may submit homeworks for grading. There will be a penalty for assignments submitted late, which is an increasing but moderate and unspecified. Within reason, it is better to submit an assignment late but complete rather than on the due date but incomplete. Homework should be submitted in class in hard copy. Homework by email will not be accepted except in very rare circumstances with prior approval of the instructor. Students will be able to access their homework grades on the NYU Blackboard system.


Most class communication will be on the NYU Blackboard site through the class message board there. Check the message board before starting any homework assignment, as there may be corrections or hints. Please post questions about the homework or the class there. You may also communicate with fellow students, setting up group meetings or exchanging ideas about homework. Please email the instructor or TA only for personal matters (schedule an appointment, request to submit an assignment late, etc.).


Students are encouraged to discuss homework exercises with each other. Each student must write the solutions himself or herself. Copying of solutions or allowing others to copy your solutions is considered cheating and will be handled according to NYU cheating policies and the more stringent policies of the math finance program. Code sharing is not allowed. You must type (or create from things you've typed using an editor) every character of code you use.

Weekly schedule (tentative)

   Date          Lecture topics
Sept. 12 Discrete probability, sigma algebras as representations of partial information, conditional expectation with respect to a sigma algebra.
Sept. 19 Discrete Markov chains, path space, transtion probabilities, evolution of probability, value functions, backward and forward equations.
Sept. 26 Random walk, Brownian motion, and the convergence of random walk to Brownian motion.
Oct. 3 The heat equation, diffusion, and the relation to Brownian motion.
Oct. 17 Integrals with respect to Brownian motion, the Ito integral.
Oct. 24 Functions of Brownian motion, Ito's lemma.
Oct. 31 Hiting times, stopping times, boundary conditions.
Nov. 7 General diffusion processes, infinitesimal mean and variance.
Nov. 14 Modeling and approximation with diffusions, Monte Carlo and simulation of diffusions.
Nov. 21 Martingales, Doob stopping time theorem, quadratic variation.
Nov. 28 Stochastic differential equations, writing diffusions as functions of Brownian motion.
Dec. 5 The relation between diffusion processes and partial differential equations of diffusion type.
Dec. 12 Change of measure and Girsanov transformations.
Dec. 14 Steady states, equilibrium, recurrence and transience.
Dec. 19 Final exam, same time, same room