Geodesic
A~refinement of asymptotics in the Prokhorov--Donsker invariance principle for integral functionals
Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 4, pp. 709-730

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An asymptotic expansion with order of accuracy $o(1/\sqrt n)$ is constructed for the distribution function (d.f.) of an integral functional of a random walk $S_n(t)$. The first stage of the proof consists of an approximation (in a certain sense) of a stochastic process distribution by that of a generalized Poisson process $\pi_n(t)$ with $o(1/\sqrt n)$ accuracy. The second stage is an investigation of d.f. asymptotics for integral functionals $\pi_n(t)$. An asymptotic expansion with $o(n^{-3/2})$ accuracy is also constructed.
Keywords: random walk, asymptotic expansion. 
@article{TVP_1995_40_4_a0,
     author = {N. K. Bakirov},
     title = {A~refinement of asymptotics in the {Prokhorov--Donsker} invariance principle for integral functionals},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {709--730},
     publisher = {mathdoc},
     volume = {40},
     number = {4},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1995_40_4_a0/}
}
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N. K. Bakirov. A~refinement of asymptotics in the Prokhorov--Donsker invariance principle for integral functionals. Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 4, pp. 709-730. http://geodesic.mathdoc.fr/item/TVP_1995_40_4_a0/