On the Kinematics of Stochastic Mechanics

  • Michele Pavon
Conference paper
Part of the Progress in Systems and Control Theory book series (PSCT, volume 23)


In a series of recent papers [P1]-[P3] we have shown that the complexification of the velocity and momentum processes permits to effectively develop a Lagrangian and Hamiltonian formalism in stochastic mechanics [N1], [G], [N2]. In this paper, the kinematics employed in [P1]-[P3] is more thoroughly analyzed, particularly from the probabilistic viewpoint. The outline of the paper is as follows. In Section 2, we introduce the appropriate kinematics for finite-energy diffusions developing on [N3]. In Section 3, we discuss in detail the properties of the quantum noise and derive a fundamental change of variables formula. In the following section, we consider the Markov case. In Section 5, for the purpose of comparison, we give a strong form of the classical Hamilton principle. In Section 6, we present the quantum Hamilton principle.


Variational Principle Quantum Noise Variable Formula Stochastic Case Stochastic Mechanic 
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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Michele Pavon
    • 1
  1. 1.Dipartimento di Elettronica e InformaticaUniversità di PadovaPadova and LADSEB-CNRItaly

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