Kinematics and Dynamics of Itô Processes

  • Laura M. Morato
Part of the International Centre for Mechanical Sciences book series (CISM, volume 261)


In this paper we deal with an extension of the Nelson’s stochastic mechanics of a quantum particle, Nelson.1 The basic Nelson’s hypothesis is that the “position variable” q(t) ∈ R3 must be interpreted as a continuous Markov process described by the stochastic differential equation
$$ dq\left( t \right) = b\left( {q\left( t \right),t} \right)dt + \left( {h/2\pi m} \right)\frac{1}{2}dw $$
with initial condition q(0)=qo, h being the Planck’s constant, m the mass of the particle and w(t) the standard Brownian motion.


Stochastic Differential Equation Quantum Particle Schrodinger Equation Standard Brownian Motion Quantum Description 
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  1. 1.
    Nelson, E., Derivation of the Schrödinger equation from Newtonian mechanics, Phys. Rev., 150, n. 4, 1966.Google Scholar
  2. 2.
    Nelson, E., Dynamical theories of Brownian motion, Princeton University Press, 1967.Google Scholar
  3. 3.
    Dankel Jr., T.G., Mechanics on manifold and incorporation of spin into Nelson’s stochastic mechanics, Arch. Rational Mech. Ann., 37, 1970.Google Scholar
  4. 4.
    Morato, L.M., Notes on stochastic mechanics, Int.Rep. LADSEB-CNR, 1978.Google Scholar

Copyright information

© Springer-Verlag Wien 1980

Authors and Affiliations

  • Laura M. Morato
    • 1
  1. 1.Istituto di Elettrotecnica ed ElettronicaUniversità di Padova and Laboratorio per Ricerche di Dinamica dei Sistemi e di Bioingegneria, C.N.R., PadovaPadovaItalia

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