2007/11/05 by Shota Gugushvili, Gugushvili, Shota
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #62G07 #62G20 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability and Risk Models #Statistics Theory (math.ST) #Stochastic processes and financial applications #math.ST #msc:62G07 #msc:62G20 #stat.TH
paper · pdf · doi:10.48550/arxiv.0711.0719
26 pages, 6 figures
arxiv created 2007/11/05 · openalex publication_date 2007/11/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Assuming that a stochastic process X=(Xt)t≥ 0 is a sum of a compound Poisson process Y=(Yt)t≥ 0 with known intensity λ and unknown jump size density f, and an independent Brownian motion Z=(Zt)t≥ 0, we consider the problem of nonparametric estimation of f from low frequency observations from X. The estimator of f is constructed via Fourier inversion and kernel smoothing. Our main result deals with asymptotic normality of the proposed estimator at a fixed point.