Ensemble and trajectory statistics in a nonlinear partial differential equation期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Ensemble and trajectory statistics in a nonlinear partial differential equation

Authors:	Michael C Mackey Helmut Schwegler

Institution:	(1) Departments of Physiology, Physics and Mathematics and Center for Nonlinear Dynamics, McGill University, H3G 1Y6 Montreal, Canada;(2) Institute of Theoretical Physics, University of Bremen, D-2800 Bremen, Germany

Abstract:	We have examined the influence of parametric noise on the solution behavioru(t, x) of a nonlinear initial value() problem arising in cell kinetics. In terms of ensemble statistics, the eventual limiting solution mean $\mathop \xi \limits^ - _u$ and variance $\mathop {\sigma _u^2 }\limits^ -$ are well-characterized functions of the noise statistics, and $\mathop \xi \limits^ - _u$ and $\mathop {\sigma _u^2 }\limits^ -$ depend on . When noise is continuously present along the trajectory, $\mathop \xi \limits^ - _u$ and $\mathop {\sigma _u^2 }\limits^ -$ are independent of the noise statistics and . However, in their evolution toward $\mathop \xi \limits^ - _u$ and $\mathop {\sigma _u^2 }\limits^ -$ , both _u (t, x) and _u ² (t, x) depend on the noise and.

Keywords:	Parametric noise nonlinear partial differential equations ensemble statistics trajectory statistics
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