In the general framework of stochastic control theory we introduce a suitable form of stochastic action associated to the controlled process. A variational principle gives all the main features of Nelson's stochastic mechanics. In particular, we derive the expression for the current velocity field as the gradient of the phase action. Moreover, the stochastic corrections to the Hamilton-Jacobi equation are in agreement with the quantum-mechanical form of the Madelung fluid (equivalent to the Schrödinger equation). Therefore, stochastic control theory can provide a very simple model simulating quantum-mechanical behavior. © 1983 The American Physical Society.
Quantization of dynamical systems and stochastic control theory / Guerra, Francesco; Laura, Morato. - In: PHYSICAL REVIEW D. - ISSN 0556-2821. - 27:8(1983), pp. 1774-1786. [10.1103/physrevd.27.1774]
Quantization of dynamical systems and stochastic control theory
GUERRA, Francesco;
1983
Abstract
In the general framework of stochastic control theory we introduce a suitable form of stochastic action associated to the controlled process. A variational principle gives all the main features of Nelson's stochastic mechanics. In particular, we derive the expression for the current velocity field as the gradient of the phase action. Moreover, the stochastic corrections to the Hamilton-Jacobi equation are in agreement with the quantum-mechanical form of the Madelung fluid (equivalent to the Schrödinger equation). Therefore, stochastic control theory can provide a very simple model simulating quantum-mechanical behavior. © 1983 The American Physical Society.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.