Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. Recently it was established that one of these likelihood ratios, which is an exponential functional of a two-sided Poisson process driven by some parameter, can be approximated (for sufficiently small values of the parameter) by another one, which is an exponential functional of a two-sided Brownian motion. In this chapter we consider yet another likelihood ratio, which is the exponent of a two-sided compound Poisson process driven by some parameter. We establish that the compound Poisson type likelihood ratio can also be approximated by the Brownian type one for sufficiently small values of the parameter. We equally discuss the asymptotics for large values of the parameter.
CITATION STYLE
Dachian, S., & Negri, I. (2013). On Gaussian compound poisson type limiting likelihood ratio process. In Studies in Theoretical and Applied Statistics, Selected Papers of the Statistical Societies (pp. 29–39). Springer International Publishing. https://doi.org/10.1007/978-3-642-35588-2_4
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