Tail estimates for stochastic fixed point equations via nonlinear renewal theory
| Autor: | Jeffrey F. Collamore, Anand N. Vidyashankar |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: |
Statistics and Probability
Path (topology) Applied Mathematics 010102 general mathematics Probability (math.PR) 16. Peace & justice Lipschitz continuity 01 natural sciences Upper and lower bounds Primary 60H25 secondary 60K05 60F10 60J10 60G70 60K25 60K35 Combinatorics 010104 statistics & probability Nonlinear system Iterated function Modeling and Simulation FOS: Mathematics Large deviations theory Renewal theory 0101 mathematics Constant (mathematics) Mathematics - Probability Mathematics |
| Zdroj: | Collamore, J F & Vidyashankar, A N 2013, ' Tail estimates for stochastic fixed point equations via nonlinear renewal theory ', Stochastic Processes and Their Applications, vol. 123, no. 9, pp. 3378-3429 . https://doi.org/10.1016/j.spa.2013.04.015 |
| DOI: | 10.1016/j.spa.2013.04.015 |
| Popis: | This paper presents precise large deviation estimates for solutions to stochastic fixed point equations of the type V =_d f(V), where f(v) = Av + g(v) for a random function g(v) = o(v) a.s. as v tends to infinity. Specifically, we provide an explicit characterization of the pair (C,r) in the tail estimate P(V > u) ~ C u^-r as u tends to infinity, and also present a Lundberg-type upper bound of the form P(V > u) 56 pages. Minor corrections (March 14, 2011) |
| Databáze: | OpenAIRE |
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