Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
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TL;DR: In this paper, local asymptotic properties of likelihood ratios of certain Heston models are studied in three cases: subcritical, critical, and supercritical models for the drift parameters.
Abstract: We study local asymptotic properties of likelihood ratios of certain Heston models We distinguish three cases: subcritical, critical and supercritical models For the drift parameters, local asymptotic normality is proved in the subcritical case, only local asymptotic quadraticity is shown in the critical case, while in the supercritical case not even local asymptotic quadraticity holds For certain submodels, local asymptotic normality is proved in the critical case, and local asymptotic mixed normality is shown in the supercritical case As a consequence, asymptotically optimal (randomized) tests are constructed in cases of local asymptotic normality Moreover, local asymptotic minimax bound, and hence, asymptotic efficiency in the convolution theorem sense are concluded for the maximum likelihood estimators in cases of local asymptotic mixed normality
6 citations
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01 Jan 2002TL;DR: In this article, the complex amplitude and the expected photon number for the thermal states were simultaneously measured for state estimation in two different cases: in one case we cannot use the quantum correlations between samples, and in the other case we can use them.
Abstract: Concerning state estimation, we will compare two cases. In one case we cannot use the quantum correlations between samples. In the other case, we can use them. In addition, under the later case, we will propose a method which simultaneously measures the complex amplitude and the expected photon number for the thermal states.
6 citations
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6 citations
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TL;DR: In this paper, asymptotic estimates for singularly perturbed boundary value problems with initial jumps were obtained for the case of single-jump boundary-value problems, where the initial jump is independent of the boundary value.
Abstract: We obtain asymptotic estimates for solutions of singularly perturbed boundary-value problems with initial jumps.
6 citations