  The purpose of this paper is to examine stochastic Markovian models for
circuits in phase space for which the drift term is equivalent to the standard
circuit equations. In particular we include dissipative components
corresponding to both a resistor and a memristor in series. We obtain a
dilation of the problem for which is canonical in the sense that the underlying
Poisson Brackets structure is preserved under the stochastic flow. We do this
first of all for standard Wiener noise, but also treat the problem using a new
concept of symplectic noise where the Poisson structure is extended to the
noise as well as the circuit variables, and in particular where we have
canonically conjugate noises. Finally we construct a dilation which describes
the quantum mechanical analogue.
