What are the latest developments and open problems in Ito calculus?

[johnqwertyful]

I've been learning Ito calculus and it seems so underdeveloped. What's new? What are the open problems? Who's working on it? What are the big developments? Anything?

 

[Simon Bridge]

I've been learning Ito calculus and it seems so underdeveloped.

In what way? Please be specific.

What's new? What are the open problems? Who's working on it? What are the big developments? Anything?

It's the extension of regular calculus to stochastic processes.
But that should have been explained in the introductory materials you are using to learn from.
http://quantum.phys.cmu.edu/QIP/ito_calculus.pdf

 

[johnqwertyful]

In what way? Please be specific.

It's the extension of regular calculus to stochastic processes.
But that should have been explained in the introductory materials you are using to learn from.
http://quantum.phys.cmu.edu/QIP/ito_calculus.pdf

I learned what SDEs are, Feynman Kac, everything in introductory materials. What else is there? What's beyond SDEs, Ito's Lemma, Feynman Kac? What are the big open problems?

 

[Simon Bridge]

That's still a bit vague - but I think I see what you are getting at.
Have a look at: http://arxiv.org/pdf/math/0409277.pdf
.. p94 has a brief discussion of Wigner Gaussian matrices and points out that relaxing the "gaussian" requirement would be a tempting generalization. How to do this, would be an "open problem" for the field.

Each chapter has more examples.
That help?