Electronic Resource
College Park, Md.
:
American Institute of Physics (AIP)
Journal of Mathematical Physics
33 (1992), S. 1695-1704
ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
The autocorrelations of the line element for the sample paths of diffusion processes are computed. Lengths are defined for the sample paths of diffusions which depend upon an arbitrary function f and reduce to the classical relativistic length for differentiable trajectories. Their mean values are computed for a general diffusion and provide a family of stochastic actions labeled by f. In a variational principle, these actions are extremized over the drift and probability density and the equations characterizing the critical diffusions are derived. The Klein–Gordon equation is obtained from the variation of arbitrary f-dependent stochastic extensions of the length of trajectories.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.529699
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