An Itô calculus for a class of limit processes arising from random walks on the complex plane

Within the framework of the previous paper (Bonaccorsi and Mazzucchi, 2015), 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.