Tail estimates for stochastic fixed point equations via nonlinear renewal theory

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Tail estimates for stochastic fixed point equations via nonlinear renewal theory. / Collamore, Jeffrey F.; Vidyashankar, Anand N.

I: Stochastic Processes and Their Applications, Bind 123, Nr. 9, 2013, s. 3378-3429.

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

Harvard

Collamore, JF & Vidyashankar, AN 2013, 'Tail estimates for stochastic fixed point equations via nonlinear renewal theory', Stochastic Processes and Their Applications, bind 123, nr. 9, s. 3378-3429. https://doi.org/10.1016/j.spa.2013.04.015

APA

Collamore, J. F., & Vidyashankar, A. N. (2013). Tail estimates for stochastic fixed point equations via nonlinear renewal theory. Stochastic Processes and Their Applications, 123(9), 3378-3429. https://doi.org/10.1016/j.spa.2013.04.015

Vancouver

Collamore JF, Vidyashankar AN. Tail estimates for stochastic fixed point equations via nonlinear renewal theory. Stochastic Processes and Their Applications. 2013;123(9):3378-3429. https://doi.org/10.1016/j.spa.2013.04.015

Author

Collamore, Jeffrey F. ; Vidyashankar, Anand N. / Tail estimates for stochastic fixed point equations via nonlinear renewal theory. I: Stochastic Processes and Their Applications. 2013 ; Bind 123, Nr. 9. s. 3378-3429.

Bibtex

@article{39bcbdeff57e4e92a383e6c70087b2c8,
title = "Tail estimates for stochastic fixed point equations via nonlinear renewal theory",
abstract = "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)~Cu^{-r} as u tends to infinity, and also present a corresponding Lundberg-type upper bound. To this end, we introduce a novel dual change of measure on a random time interval and analyze the path properties, using nonlinear renewal theory, of the Markov chain resulting from the forward iteration of the given stochastic fixed point equation. In the process, we establish several new results in the realm of nonlinear renewal theory for these processes. As a consequence of our techniques, we also establish a new characterization of the extremal index. Finally, we provide some extensions of our methods to Markov-driven processes.",
author = "Collamore, {Jeffrey F.} and Vidyashankar, {Anand N.}",
year = "2013",
doi = "10.1016/j.spa.2013.04.015",
language = "English",
volume = "123",
pages = "3378--3429",
journal = "Stochastic Processes and their Applications",
issn = "0304-4149",
publisher = "Elsevier BV * North-Holland",
number = "9",

}

RIS

TY - JOUR

T1 - Tail estimates for stochastic fixed point equations via nonlinear renewal theory

AU - Collamore, Jeffrey F.

AU - Vidyashankar, Anand N.

PY - 2013

Y1 - 2013

N2 - 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)~Cu^{-r} as u tends to infinity, and also present a corresponding Lundberg-type upper bound. To this end, we introduce a novel dual change of measure on a random time interval and analyze the path properties, using nonlinear renewal theory, of the Markov chain resulting from the forward iteration of the given stochastic fixed point equation. In the process, we establish several new results in the realm of nonlinear renewal theory for these processes. As a consequence of our techniques, we also establish a new characterization of the extremal index. Finally, we provide some extensions of our methods to Markov-driven processes.

AB - 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)~Cu^{-r} as u tends to infinity, and also present a corresponding Lundberg-type upper bound. To this end, we introduce a novel dual change of measure on a random time interval and analyze the path properties, using nonlinear renewal theory, of the Markov chain resulting from the forward iteration of the given stochastic fixed point equation. In the process, we establish several new results in the realm of nonlinear renewal theory for these processes. As a consequence of our techniques, we also establish a new characterization of the extremal index. Finally, we provide some extensions of our methods to Markov-driven processes.

U2 - 10.1016/j.spa.2013.04.015

DO - 10.1016/j.spa.2013.04.015

M3 - Journal article

VL - 123

SP - 3378

EP - 3429

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

IS - 9

ER -

ID: 109552199