We introduce the concept of Poisson Brackets for classical noise and, in particular, for pairs of canonically conjugate Wiener processes (symplectic noise). Phase space diffusions driven by these processes are considered and the general form of a stochastic process preserving the full (system and noise) Poisson structure is obtained. Making the requirement that the classical stochastic model preserves the joint system and noise Poisson Brackets, we show that the model has actually much in common with quantum markovian models.
|Journal||Journal of Statistical Physics|
|Early online date||28 Jun 2015|
|Publication status||Published - Sept 2015|
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