Kinematics and Dynamics of Itô Processes

Abstract

In this paper we deal with an extension of the Nelson’s stochastic mechanics of a quantum particle, Nelson.1 The basic Nelson’s hypothesis is that the “position variable” q(t) ∈ R3 must be interpreted as a continuous Markov process described by the stochastic differential equation $$ dq\left( t \right) = b\left( {q\left( t \right),t} \right)dt + \left( {h/2\pi m} \right)\frac{1}{2}dw $$ with initial condition q(0)=qo, h being the Planck’s constant, m the mass of the particle and w(t) the standard Brownian motion.