Derivatives of the stochastic growth rate.
We consider stochastic matrix models for population driven by random environments which form a Markov chain. The top Lyapunov exponent a, which describes the long-term growth rate, depends smoothly on the demographic parameters (represented as matrix entries) and on the parameters that define the st...
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| Format: | Journal article |
| Language: | English |
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2011
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| _version_ | 1797098809982976000 |
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| author | Steinsaltz, D Tuljapurkar, S Horvitz, C |
| author_facet | Steinsaltz, D Tuljapurkar, S Horvitz, C |
| author_sort | Steinsaltz, D |
| collection | OXFORD |
| description | We consider stochastic matrix models for population driven by random environments which form a Markov chain. The top Lyapunov exponent a, which describes the long-term growth rate, depends smoothly on the demographic parameters (represented as matrix entries) and on the parameters that define the stochastic matrix of the driving Markov chain. The derivatives of a-the "stochastic elasticities"-with respect to changes in the demographic parameters were derived by Tuljapurkar (1990). These results are here extended to a formula for the derivatives with respect to changes in the Markov chain driving the environments. We supplement these formulas with rigorous bounds on computational estimation errors, and with rigorous derivations of both the new and old formulas. |
| first_indexed | 2024-03-07T05:14:59Z |
| format | Journal article |
| id | oxford-uuid:dcdb51e3-82e7-47c6-a63b-7ccf65a63e91 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:14:59Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | oxford-uuid:dcdb51e3-82e7-47c6-a63b-7ccf65a63e912022-03-27T09:20:46ZDerivatives of the stochastic growth rate.Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:dcdb51e3-82e7-47c6-a63b-7ccf65a63e91EnglishSymplectic Elements at Oxford2011Steinsaltz, DTuljapurkar, SHorvitz, CWe consider stochastic matrix models for population driven by random environments which form a Markov chain. The top Lyapunov exponent a, which describes the long-term growth rate, depends smoothly on the demographic parameters (represented as matrix entries) and on the parameters that define the stochastic matrix of the driving Markov chain. The derivatives of a-the "stochastic elasticities"-with respect to changes in the demographic parameters were derived by Tuljapurkar (1990). These results are here extended to a formula for the derivatives with respect to changes in the Markov chain driving the environments. We supplement these formulas with rigorous bounds on computational estimation errors, and with rigorous derivations of both the new and old formulas. |
| spellingShingle | Steinsaltz, D Tuljapurkar, S Horvitz, C Derivatives of the stochastic growth rate. |
| title | Derivatives of the stochastic growth rate. |
| title_full | Derivatives of the stochastic growth rate. |
| title_fullStr | Derivatives of the stochastic growth rate. |
| title_full_unstemmed | Derivatives of the stochastic growth rate. |
| title_short | Derivatives of the stochastic growth rate. |
| title_sort | derivatives of the stochastic growth rate |
| work_keys_str_mv | AT steinsaltzd derivativesofthestochasticgrowthrate AT tuljapurkars derivativesofthestochasticgrowthrate AT horvitzc derivativesofthestochasticgrowthrate |