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How do you get from calculus to stochastic calculus? 
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#1
Oct1705, 01:54 AM

P: 29

What is the path of study to understand stochastic calculus? I bought the book "Elementary Stochastic Calculus with Finance in View" (Mikosch) because it was touted as a non rigorous introduction to stochastic calculus, and I spent three days trying to decipher the first two pages. :(



#2
Oct1705, 05:27 PM

P: 333

What level of mathematics education have you reached? You probably ought to have at least some level of familiarity with measuretheoretic probabality theory. What was the content of the first two pages?



#3
Oct1905, 04:04 AM

P: 29

[itex]X=X(\omega)\epsilon\{0,1\}[/itex] where [itex]\displaystyle\omega[/itex] belongs to the outcome space [itex]\Omega=\{heads, tails\}[/itex] After I deciphered the notation, that seemed straightforward enough. But, then under the innocuous subheading: "Which are the most likely [itex]X(\omega)[/itex], what are they concentrated around, what are their spread? the book says that to approach those problems, one first collects "good" subsets of [itex]\Omega[/itex] in a class F, where F is a [itex]\sigma[/itex]field. Such a class is supposed to contain all interesting events. Certainly, {w:X(w)=0}={tail} and {w:X(w)=1}={head} must belong to F, but also the union, difference, and intersection of any events in F and its complement the empty set. If A is an element of F, so is it's complement, and if A,B are elements of F, so are A intersection B, A union B, A union B complement, B union A complement, A intersection B complement, B intersection A complement, etc. Whaaa? What's all that [itex]\sigma[/itex]field stuff got to do with the probabilites of X(w)? Also, if A and B are a member of a class F, isn't A union B also automatically a member of the class F, as well as A intersection B, etc.? 


#4
Oct1905, 08:46 AM

P: 333

How do you get from calculus to stochastic calculus?
Take a peek at http://www.math.uconn.edu/~bass/lecture.html. I had a look around amazon and couldn't find anything like a nonrigourous book on the subject, and most of the books seem a bit pricey considering that you'll only be reading one or two chapters from them. Have a look at those notes and see how you get on.



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