TITLE: Background for studying and understanding Stochastic differential equations
QUESTION [6 upvotes]: Assume I have back ground of the following knowledge based on the textbook as :
ODE : ODE by Tenenbaum
Baby probability : Ross 's baby probability
Baby real anlysis : Bartle's introduction to real analysis (1st undergrad course in advanced cal)
Baby measure theory : Bartle 's element of Lebesgue measure and integration
1 course of undergrad linear algebra, and cal 1-3
what specific areas of math would I need to learn more in order to understand the SDE book of Oksendal : Stochastic Differential Equations: An Introduction with Applications . Many thanks for the suggestion about my background. I will take the 1st graduate course of SDE in the Spring

REPLY [5 votes]: My two cents... 
Put aside all the measure/analysis textbooks. When you learnt calculus in college or high-school you did not have to learn analysis right then, isn't it? 
So focus on getting a good understanding of Ito calculus first. 
Focus on being able to compute stuff. 
Pay attention on the "how to" and not on the "why". 
Go to a library and check out these two books: 

Dynamic Optimization: The Calculus of Variations and Optimal Control 
By Morton I. Kamien, Nancy L. Schwartz (see last chapters only)
The Art of Smooth Pasting By Avinash K. Dixit