Stochastic nonlinear Perron–Frobenius theorem

Stochastic nonlinear Perron–Frobenius theorem We establish a stochastic nonlinear analogue of the Perron–Frobenius theorem on eigenvalues and eigenvectors of positive matrices. The result is formulated in terms of an automorphism T of a probability space and a random transformation D of the non-negative cone of an n-dimensional Euclidean space. Under assumptions of monotonicity and homogeneity of D, we prove the existence of scalar and vector measurable functions α > 0 and x > 0 satisfying the equation αTx = D(x) almost surely. We apply the result obtained to the analysis of a class of random dynamical systems arising in mathematical economics and finance (von Neumann–Gale dynamical systems). Positivity Springer Journals

Stochastic nonlinear Perron–Frobenius theorem

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SP Birkhäuser Verlag Basel
Copyright © 2009 by Birkhäuser Verlag Basel/Switzerland
Mathematics; Econometrics; Calculus of Variations and Optimal Control; Optimization; Potential Theory; Operator Theory; Fourier Analysis
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