Can a stochastic process be chaotic?

[wathan]

Can we consider a stochastic process being chaotic?

consider evolution of only two particular systems with closed initial states (not ensemble or statistical properties of the system)

 

[Andy Resnick]

Not in general- a 'chaotic' system has specific properties associated with it.

 

[maxplankj]

The hamiltonian of a stochastic system have a random variable so the solutions of the hamilton equations cannot be deterministic. The hamiltonians of a chaotics systems do not have random variable so the solutions of the hamilton equations are deterministic. You have to transform your deterministic hamiltonian into a hamiltonian with a random variable and I think that is imposible.