2015/06/26 by Paul Ilhe, Ilhe, Paul, Éric Moulines +5
Economics, Econometrics and Finance · Mathematics · #Applications (stat.AP) #FOS: Computer and information sciences #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistical Methods and Inference #Statistics Theory (math.ST) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1506.08047
openalex publication_date 2015/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider a nonlinear inverse problem occurring in nuclear\nscience. Gamma rays randomly hit a semiconductor detector which produces an\nimpulse response of electric current. Because the sampling period of the\nmeasured current is larger than the mean inter arrival time of photons, the\nimpulse responses associated to different gamma rays can overlap: this\nphenomenon is known as pileup. In this work, it is assumed that the impulse\nresponse is an exponentially decaying function. We propose a novel method to\ninfer the distribution of gamma photon energies from the indirect measurements\nobtained from the detector. This technique is based on a formula linking the\ncharacteristic function of the photon density to a function involving the\ncharacteristic function and its derivative of the observations. We establish\nthat our estimator converges to the mark density in uniform norm at a\nlogarithmic rate. A limited Monte-Carlo experiment is provided to support our\nfindings.\n