Frequently Asked Questions about Stochastic Calculus, fall term, 2004 course home page: http://www.math.nyu.edu/faculty/goodman/teaching/StochCalc2004/index.html What is Stochastic Calculus? Ways to calculate things about random processes. This course starts with simple discrete models and moves to continuous models where the tools are stochastic integrals, stochastic differential equations, and partial differential equations. For whom is the course intended? Primarily students in the Courant Institute program in Financial Mathematics. All graduate students at the Courant Institute and elsewhere within NYU may enroll. However, this is a serious math class with serious prerequisites (see the web page). Is the class only for people interested in applications to finance? No. The tools of Stochastic Calculus apply to many problems outside finance or economics. The current interest in Stochastic Calculus is largely because of its appications in finance, which will play a major role in the class. Will the class be rigorous in the mathematical sense? Not completely. We will avoid technical issues such as completeness and separability of the space of continuous functions and countable additivity of the Borel sets. We will discuss major topics such as progressive measurability as a way to formulate issues of decision making with incomplete information. Do I have to attend the problem sessions? No. No new material is introduced in the problem sessions. The TA will answer questions about the material and homeworks. However, many students have found the material and homeworks very challenging, so the problem sessions may make the difference between success and its alternative. If I am not currently a Courant Institute graduate student, how do I enroll? That depends on who you are. Contact Gabrielle Maloney (maloney@cims.nyu.edu) as soon as possible if you are uncertain. Non NYU students will need to enroll in NYU in some way, possibly as a "nondegree" graduate student. What is the text? to be determined What are the prerequisites? A solid course in calculus based probability, together with multivariate calculus and linear algebra. You should be comfortable working with probability densities, integrating to get means and variances, computing conditional probabilities, etc. You should be able to do this with "multivariate" random variables given by a joint probability density in more than one dimension, computing marginal and conditional probability densities, means and conditional means, covariances, etc. You should understand the law of large numbers and the central limit theorem and be able to apply them. Independence of random variables and Bayes' rule play a big role. What if my background is rusty? If your probability needs oiling, make sure to do this before the first class. You can find out by completing the first homework assingment, which is posted on the class web page. This assignment is due on the first day of class. If you need a quick review a good source is books in the Schaum's outline series. There is a Schaum's Outline of Probability, a Schaum's outline of Linear Algebra, and an outline on multivariate calculus (the outline on vector calculus is less relevent). If you need to learn or re learn some topics, there are several excellent undergraduate probability books. One is "Introduction to Probability" by Dimitri Bertsekas and John Tsitkiklis, , especially chapters 1-4 and 7. You also might try the books by Ross, Rota, and Grimmett (a bit more advanced).