Large deviations for multidimensional state-dependent shot-noise processes
2015 ◽
Vol 52
(4)
◽
pp. 1097-1114
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Keyword(s):
Shot-noise processes are used in applied probability to model a variety of physical systems in, for example, teletraffic theory, insurance and risk theory, and in the engineering sciences. In this paper we prove a large deviation principle for the sample-paths of a general class of multidimensional state-dependent Poisson shot-noise processes. The result covers previously known large deviation results for one-dimensional state-independent shot-noise processes with light tails. We use the weak convergence approach to large deviations, which reduces the proof to establishing the appropriate convergence of certain controlled versions of the original processes together with relevant results on existence and uniqueness.
2015 ◽
Vol 52
(04)
◽
pp. 1097-1114
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2011 ◽
Vol 48
(03)
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pp. 688-698
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2010 ◽
Vol 80
(15-16)
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pp. 1200-1209
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2005 ◽
Vol 10
(0)
◽
pp. 1026-1043
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Keyword(s):
Keyword(s):
Exponential martingale and large deviations for a Cox risk process with Poisson shot noise intensity
2012 ◽
Vol 394
(1)
◽
pp. 74-83
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Keyword(s):
2018 ◽
Vol 50
(3)
◽
pp. 983-1004
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