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Exponential asymptotics for nonlinearly perturbed renewal equation with non-polynomial perturbationsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2008 (English)In: Journal of Numerical and Applied Mathematics, ISSN 0868-6912, Vol. 96, no 1, p. 173-197Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Kiev: TBiMC , 2008. Vol. 96, no 1, p. 173-197
##### Keywords [en]

Renewal equation, nonlinear perturbation, non-polynomial perturbation, exponential asymptotic expansion, risk process, ruin probability
##### National Category

Probability Theory and Statistics Mathematics
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

URN: urn:nbn:se:mdh:diva-5285OAI: oai:DiVA.org:mdh-5285DiVA, id: diva2:160339
#####

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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt466",{id:"formSmash:j_idt466",widgetVar:"widget_formSmash_j_idt466",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt472",{id:"formSmash:j_idt472",widgetVar:"widget_formSmash_j_idt472",multiple:true}); Available from: 2009-02-13 Created: 2009-02-13 Last updated: 2015-06-29Bibliographically approved
##### In thesis

The model of nonlinearly perturbedcontinuous-time renewal equation is studied in this paper.The perturbation conditions considered involve asymptoticalexpansions with respect to asymptotic scale$\{\varphi_{n,m}(\varepsilon) = \varepsilon^{n +m\omega}\}$,with $n, m$ being non-negative integers and $\omega >1$ beingirrational number. Such asymptotical scale results in non-polynomialtype of asymptotic expansions for solutions for perturbed renewalequations. An example of risk processes with perturbations describedabove and asymptotic expansions in diffusion approximation for ruinprobabilities in this model are given.

1. Perturbed Renewal Equations with Non-Polynomial Perturbations$(function(){PrimeFaces.cw("OverlayPanel","overlay302104",{id:"formSmash:j_idt793:0:j_idt800",widgetVar:"overlay302104",target:"formSmash:j_idt793:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Nonlinearly Perturbed Renewal Equations: asymptotic Results and Applications$(function(){PrimeFaces.cw("OverlayPanel","overlay438488",{id:"formSmash:j_idt793:1:j_idt800",widgetVar:"overlay438488",target:"formSmash:j_idt793:1:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

urn-nbn$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_j_idt1275",{id:"formSmash:j_idt1275",widgetVar:"widget_formSmash_j_idt1275",showEffect:"fade",hideEffect:"fade",showDelay:500,hideDelay:300,target:"formSmash:altmetricDiv"});});

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