Stochastic Nonlinear Perron-frobenius Theorem∗
نویسنده
چکیده
We establish a stochastic nonlinear analogue of the PerronFrobenius theorem on eigenvalues and eigenvectors of positive matrices. The result is formulated in terms of an automorphism T of a probability space (Ω,F , P ) and a random mapping D(ω, ·) : R+ → R+. Under assumptions of monotonicity and homogeneity of D(ω, ·), we prove the existence of scalar and vector measurable functions α(ω) > 0 and x(ω) > 0 satisfying the equation α(ω)x(Tω) = D(ω, x(ω)) almost surely.
منابع مشابه
PERRON-FROBENIUS THEORY ON THE NUMERICAL RANGE FOR SOME CLASSES OF REAL MATRICES
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