An asymptotic factorization of the Small–Ball Probability: theory and estimates

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.