Actually what I want to know is 'is it possible to define a directional derivative as in the calculus. (something like Gradient operator)'

Probably the functional Ito Calculus may help you. There are two main works, one by Bruno Dupire and the other by Cont and Fournie.

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1435551

http://projecteuclid.org/download/pdfview_1/euclid.aop/1358951982

Hope these will be helpful!

Best

Logic tells us that if you can define ordinary derivative in stochastic calculus in 1D space you can easily generalized it into 3D in terms of Gradient operator without having any further restriction on the system.   While doing that one should keep in mind that only the expectation values of the random variable or function are matters, which behave like:

 Ordinary variables and functions in calculus.

Directional  Derivative of:  a  = a. Grad = (a.Grad) ,

                                                               ={ L pDx + M pDy  + N pDz}  . Where L,M,N  are the direction cosines of  a   relative to the coordinate axes, pDx,yz  partial differential derivative operators.Bold letters indicate vectorial quantities here.

In ITO  calculus  so-called  independent  variables Xt and  Ys are implicit functions  of time over the well defined paths.   Therefore one has to be little  careful in the new definitions pD  and Grad operator.  Dr. Maggis referred very valuable references in this respect. Where path dependence symbolical taking care of using  different letters such as  X. Y..Z with subscribe t, s etc.  for the same variable, which are  tracking different paths in time domain.