The purpose of this note is to identify an interesting and surprising duality between the equations governing the probability distribution and expected value functional of the stochastic process deΓΏned by At := t 0 exp{Zs} ds; t ΒΏ 0; where {Zs: s ΒΏ 0} is a one-dimensional Brownian motion with drift
A note on the systematic integration of Kramers' equation for brownian motion in a field of force
β Scribed by R.O. Davies
- Publisher
- Elsevier Science
- Year
- 1957
- Weight
- 87 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0031-8914
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π SIMILAR VOLUMES
K r a m e r s 1) has derived a diffusion equation in phase space, describing the motion of a particle subject to an external force and to the shuttling action of the Brownian forces caused by a surrounding medium in temperature equilibrium. In this paper a solution of Kramers' equation is obtained
We study the effect of a field on the span of a particle diffusing on a line, i.e., the length covered by a Brownian particle which moves on a line for time t in the presence of a constant field. This is the one-dimensional analog of the Wiener sausage volume. Exact expressions are found for the pro
H. A. Kr a m e r s 1) has studied the rate of chemical reactions in view of the Brownian forces caused by a surrounding medium in temperature equilibrium. In a previous paper 3) the author gave a solution of Kramers' diffusion equation in phase space by systematic development. In this paper the gene