Langevin equations with multiplicative noise: Resolution of time discretization ambiguities for equilibrium systems
- Department of Physics, University of Virginia, Charlottesville, Virginia 22901 (United States)
A Langevin equation with multiplicative noise is an equation schematically of the form dq/dt=-F(q)+e(q){xi}, where e(q){xi} is Gaussian white noise whose amplitude e(q) depends on q itself. Such equations are ambiguous, and depend on the details of one's convention for discretizing time when solving them. I show that these ambiguities are uniquely resolved if the system has a known equilibrium distribution exp[-V(q)/T] and if, at some more fundamental level, the physics of the system is reversible. I also discuss a simple example where this happens, which is the small frequency limit of Newton's equation qe+e{sup 2}(q)q=-{nabla}V(q)+e{sup -1}(q){xi} with noise and a q-dependent damping term. The resolution does not correspond to simply interpreting naive continuum equations in a standard convention, such as Stratonovich or Ito. (c) 2000 The American Physical Society.
- OSTI ID:
- 20216770
- Journal Information:
- Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 61, Issue 6; Other Information: PBD: Jun 2000; ISSN 1063-651X
- Country of Publication:
- United States
- Language:
- English
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