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Author Herzog, David P
Title Geometry's fundamental role in the stability of stochastic differential equations
book jacket
Descript 108 p
Note Source: Dissertation Abstracts International, Volume: 72-07, Section: B, page: 4053
Adviser: Jan Wehr
Thesis (Ph.D.)--The University of Arizona, 2011
We study dynamical systems in the complex plane under the effect of constant noise. We show for a wide class of polynomial equations that the ergodic property is valid in the associated stochastic perturbation if and only if the noise added is in the direction transversal to all unstable trajectories of the deterministic system. This has the interpretation that noise in the "right" direction prevents the process from being unstable: a fundamental, but not well-understood, geometric principle which seems to underlie many other similar equations. In view of [Has80, JK85, Jur97, MT93b, RB06, SV72], the result is proven by using Lyapunov functions and geometric control theory
School code: 0009
Host Item Dissertation Abstracts International 72-07B
Subject Applied Mathematics
Physics, Elementary Particles and High Energy
Alt Author The University of Arizona. Mathematics
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