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Sensitivity analysis of one parameter semigroups exemplified by the Wright--Fisher diffusion | | Peter Pfaffelhuber
; Heinz Weisshaupt
; | | Date: |
11 Apr 2011 | | Abstract: | We consider the sensitivity, with respect to a parameter heta, of
parametric families of operators A_{ heta}, vectors pi_{ heta} corresponding
to the adjoints A_{ heta}^{*} of A_{ heta} via A_{ heta}^{*}pi_{ heta}=0
and one parameter semigroups tmapsto e^{tA_{ heta}}. We display formulas
relating weak differentiability of hetamapsto pi_{ heta} (at heta=0) to
weak differentiability of hetamapsto A_{ heta}^{*}pi_{0} and
[e^{A_{ heta}t}]^{*}pi_{0}. We give two applications: The first one concerns
the sensitivity of the Ornstein--Uhlenbeck process with respect to its location
parameter. The second one provides new insights regarding the Wright--Fisher
diffusion for small mutation parameter. | | Source: | arXiv, 1104.1876 | | Services: | Forum | Review | PDF | Favorites | |
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