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).