Timeline for Teaching stochastic calculus to students who know no measure theory (or PDE, or...)
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 3, 2015 at 9:52 | comment | added | mdg | Oksendel Stochastic Differential Equations is the other standard introductory book. | |
| Feb 3, 2015 at 9:44 | comment | added | mdg | This is a very good answer. Also consider Lin Introductory Stochastic Analysis for Finance and Insurance. | |
| Nov 28, 2014 at 20:42 | comment | added | fedja | As to "do you really want to discuss tightness of probability measures in such a class?", the answer is "certainly not!", but, as I showed above, all I need to construct a Brownian motion is an a.s. convergence (uniform on bounded subsets of dyadic rationals, in my case) and that's precisely the level at which I want to keep the whole story. | |
| Nov 28, 2014 at 20:23 | comment | added | fedja | Exactly. I do not say that we disagree much on anything, rather wonder what exactly those "other sources to amend the book" are. :-) Of course, "alternatives" are of interest too. | |
| Nov 28, 2014 at 19:59 | comment | added | Stephan Sturm | I agree that he sweeps some things under the rug, one could add his treatment of quadratic variation or the non-treatment of local martingales (a quite important topic even for option pricing, e.g. in local and stochastic volatility models). But the balance between ease of exposition and rigor is hard to strike (do you really want to discuss tightness of probability measures in such a class?) and I think he is doing a very good job. I feel amending a textbook by other sources is now easier than ever, as many textbooks are in electronic form available for students for free... | |
| Nov 28, 2014 at 19:14 | comment | added | fedja | Thanks a lot. Steve's book certainly has a good order of exposition, which I may well adopt. Still, it looks like he sweeps too many things under the rug. The most amazing blunder is that he never bothers to prove that Brownian motions do, indeed, exist while (unless you invoke very heavy tools that are way beyond the scope of this course) passing directly from the existence of the limiting distribution for a family of stochastic processes to the existence of a stochastic process with the limiting distribution is not for the weak of heart, unless I miss something. | |
| Nov 28, 2014 at 18:55 | history | answered | Stephan Sturm | CC BY-SA 3.0 |