An It\^o calculus for a class of limit processes arising from random   walks on the complex plane
  Within the framework of the previous paper [8]. we develop a generalized stochastic calculus for processes associated to higher order diffusion operators. Applications to the study of a Cauchy problem, a Feynman-Kac formula and a representation formula for higher derivatives of analytic functions are also given. 
Stefano Bonaccorsi, Craig Calcaterra, Sonia Mazzucchi
math.PR