Cesaro Limits of Analytically Perturbed Stochastic Matrices
Let P(ε) = P0 + A(ε) be a stochasticity preserving analytic perturbation of a stochastic matrix P0. We characterize the hybrid Cesaro limit lim 1 N(ε) Pk(ε), ε↓0 N(ε) ∑ where N(ε) ↑ ∞ as ε ↓ 0, when P0 has eigenvalues on the unit circle in the complex plane other than 1.
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| Format: | Others |
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Scholarship @ Claremont
2005
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| Online Access: | https://scholarship.claremont.edu/hmc_theses/174 https://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1177&context=hmc_theses |
| Summary: | Let P(ε) = P0 + A(ε) be a stochasticity preserving analytic perturbation of a stochastic matrix P0. We characterize the hybrid Cesaro limit lim 1 N(ε) Pk(ε), ε↓0 N(ε) ∑ where N(ε) ↑ ∞ as ε ↓ 0, when P0 has eigenvalues on the unit circle in the complex plane other than 1. |
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