Geodesic
Exact $L_2$-small ball asymptotics for some Durbin processes
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 26, Tome 466 (2017), pp. 211-233

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We find the exact $L_2$-small ball asymptotics for some Durbin processes. These processes are finite dimentional perturbations of the Brownian bridge $B(t)$ and naturally appear in statistics as limit ones when building goodness-of-fit tests of $\omega^2$-type for testing a sample for some distribution with estimated parameters. Earlier, in the work of Nazarov and Petrova, Kac–Kiefer–Wolfowitz processes (which correspond for testing normality) were considered, where a technique for obtaining asymptotics of oscillating integrals with a slowly varying amplitude was developed. Due to this, it is possible to calculate the asymptotics of small deviations for Durbin processes for certain distributions (Laplace, logistic, Gumbel, gamma). 
@article{ZNSL_2017_466_a14,
     author = {Yu. P. Petrova},
     title = {Exact $L_2$-small ball asymptotics for some {Durbin} processes},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {211--233},
     publisher = {mathdoc},
     volume = {466},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_466_a14/}
}
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Yu. P. Petrova. Exact $L_2$-small ball asymptotics for some Durbin processes. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 26, Tome 466 (2017), pp. 211-233. http://geodesic.mathdoc.fr/item/ZNSL_2017_466_a14/