In:
American Journal of Physics, American Association of Physics Teachers (AAPT), Vol. 64, No. 10 ( 1996-10-01), p. 1246-1257
Abstract:
A novel derivation of the Langevin equation that was recently presented in this journal for a univariate continuous Markov process is generalized here to the more widely applicable multivariate case. The companion multivariate forward and backward Fokker–Planck equations are also derived. The derivations require just a few modest assumptions, and are driven by a self-consistency condition and some established theorems of random variable theory and ordinary calculus. The constructive nature of the derivations shows why a multivariate continuous Markov process must evolve according to equations of the canonical Langevin and Fokker–Planck forms, and also sheds new light on some uniqueness issues. The need for self-consistency in the time-evolution equations of both Markovian and non-Markovian stochastic processes is emphasized, and it is pointed out that for a great many non-Markovian processes self-consistency can be ensured most easily through the multivariate Markov theory.
Type of Medium:
Online Resource
ISSN:
0002-9505
,
1943-2909
Language:
English
Publisher:
American Association of Physics Teachers (AAPT)
Publication Date:
1996
detail.hit.zdb_id:
1472799-7
detail.hit.zdb_id:
2947-6
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