Geodesic
The fibre method and its application to the investigation of functionals of stochastic processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 27 (1982) no. 1, pp. 67-80

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Let $W(t)$, $t\in[0,1]$ be a standard Wiener process. The distribution of the functional $$ J=\int_0^1g(W(t),t)\,dt $$ is considered. Some conditions are found under which the distribution of $J$ has a bounded density. Some estimates of this density for large values of $J$ are given. 
@article{TVP_1982_27_1_a6,
     author = {M. A. Lif\v{s}ic},
     title = {The fibre method and its application to the investigation of functionals of stochastic processes},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {67--80},
     publisher = {mathdoc},
     volume = {27},
     number = {1},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1982_27_1_a6/}
}
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M. A. Lifšic. The fibre method and its application to the investigation of functionals of stochastic processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 27 (1982) no. 1, pp. 67-80. http://geodesic.mathdoc.fr/item/TVP_1982_27_1_a6/