Abstract
This work reviews recent results on an asymptotic factorization of the Small–Ball Probability of a \( {\fancyscript{L}}_{[0,1]}^{2} \)–valued process, as the radius of the ball tends to zero. This factorization involves a volumetric term, a pseudo–density for the probability law of the process, and a correction factor. Estimators of the latter two factors are introduced and some of their theoretical properties considered.
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Aubin, JB., Bongiorno, E.G., Goia, A. (2017). An asymptotic factorization of the Small–Ball Probability: theory and estimates. In: Aneiros, G., G. Bongiorno, E., Cao, R., Vieu, P. (eds) Functional Statistics and Related Fields. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-55846-2_7
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DOI: https://doi.org/10.1007/978-3-319-55846-2_7
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