On the differentiability of parametrized families of linear operators and the sensitivity of their stationary vectors (Q624236)
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scientific article; zbMATH DE number 5848591
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the differentiability of parametrized families of linear operators and the sensitivity of their stationary vectors |
scientific article; zbMATH DE number 5848591 |
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On the differentiability of parametrized families of linear operators and the sensitivity of their stationary vectors (English)
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8 February 2011
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In this article, the differentiability of functions of stationary vectors associated to operator-valued functions as well as the differentiability of the operator-valued functions themselves is studied. In particular, it is shown that the derivative of a weakly differentiable parametric family of continuous operators is again a parametric family of continuous operators. This result is then applied to kernel operators. Further, the sensitivity of continuous linear operators and the sensitivity of their stationary vectors is investigated.
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differentiation
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operator-valued functions
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stationary vectors
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stationary distributions
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differentiation of operators
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differentiation of Markov kernels
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measure-valued differentiation
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