Has anyone ever won a field medal for inventing stochastic calculus? I somehow wondered today why was Ito never awarded a Fields medal for inventing Ito calculus?
I also wonder has anyone ever been awarded a Fields medal for building the foundation of stochastic calculus? or has anyone won a Fields medal for research on stochastic calculus?
EDIT: 
If people actually read the answer as given, I think it is rather factual. Also, I find it totally ridiculous that people have voted to close AFTER I have accepted an answer.
 A: 
why was Ito never awarded a field Fields medal for inventing Ito calculus?

A part of the explanation is that, due to WWII, only the three first ICMs (in 1936, 1950 and 1954) were held before 1955, when Itô (born in 1915) reached the age limit of 40. Plus, Itô was not seen as an early genius at the time, his contributions being somewhat more slowly recognized than others'. Plus, the fact that at the time probability theory was regarded as "true" mathematics mainly in the USSR, also in Japan and in some circles in France, much less so in the US and in other countries.
And really, the medalists in 1936, 1950 and 1954 (to limit oneself to the ICMs held before Itô reached 40) are considered as mathematical giants still today, no? (With the exception of Douglas, perhaps, who seems to be more rarely mentioned or remembered than the others, nowadays.)

has anyone ever been awarded a field Fields medal for building the foundation of stochastic calculus?

No. This would have been Itô.

has anyone won a field Fields medal for research on stochastic calculus?

No.
Note that probability theory in the wide sense is definitely on the radar of the Fields committee these days, with medals awarded to Werner in 2006 and to Smirnov in 2010 (but, to stay focused on your question, neither of these two is mainly concerned with stochastic calculus).
A: The Fields medal was first awarded in $1936$, and is awarded every four years, each time to at most four people, so there haven't been that many Fields medallists. A complete list including an indication of their area of primary research is given in a table here. Even though no person has anything involving "stochastic" listed in their primary research entry, there might be someone whose contributions included stochastic calculus.
