Harris flow

Harris flow

[′har·əs ‚flō]
(electronics)
Electron flow in a cylindrical beam in which a radial electric field is used to overcome space charge divergence.
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A Brownian stochastic flow {x(u, t), u [member of] R, t [greater than or equal to] 0} is called a Harris flow with covariance function r if for any u, v [member of] R the joint quadratic variation of the martingales {x(u, t), t [greater than or equal to] 0} and {x(v, t), t [greater than or equal to] 0} is given by
It is easy to check that the random field {x(u, t), u [member of] R, t [greater than or equal to] 0} is a Harris flow with covariance function r given by
Let {x(u, t), u [member of] R, t [greater than or equal to] 0} be a Harris flow with covariance function [GAMMA], which has compact support, and {[x.sub.0](u, t),u [member of] R, t [greater than or equal to] 0} be the Arratia flow.
Let us note that the stochastic processes {([z.sub.n]([u.sub.1,t]), ..., [z.sub.n](un,t)), t [greater than or equal to] 0} and {([z.sub.0,n]([u.sub.1], t), ..., [z.sub.0,n]([u.sub.n], t)), t [greater than or equal to] 0} constructed according to the procedure described above (with the just defined [epsilon]) for the Harris flow {x(u, t), u [member of] R, t [greater than or equal to] 0} and the Arratia flow {[x.sub.0](u, t), u [member of] R, t [greater than or equal to] 0} respectively have the same distribution.
In this paper we study the Wasserstein distance between the distributions of the n-point motions of one-dimensional Harris flows whose covariance functions have compact support.
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