Frequently Asked Questions about 

    Stochastic Calculus, Spring term, 2007

course home page: 
http://www.math.nyu.edu/faculty/goodman/teaching/StochCalc2007/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 Melissa Kushner 
  (kushner "at" 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?

   Lecture notes will be posted.  Check the class from 2004 for preliminary
   versions of the notes.

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).