Geodesic
On sojourn times for functions and stochastic processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 3, pp. 650-654

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For processes with $d$-dimensional ($d>1$) parameter and with realizations in the class Lip 1, sufficient conditions for the existence of the density of a sojourn time are given. If realizations of the process are in the class $C^d$ ($[0,1]^d$), these conditions are also necessary. For analogs of the Brownian motion with $d$-dimensional parameter, estimates for the smoothness of the sojourn time density are obtained. 
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     author = {Yu. A. Davydov and A. L. Rozin},
     title = {On sojourn times for functions and stochastic processes},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {650--654},
     publisher = {mathdoc},
     volume = {23},
     number = {3},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1978_23_3_a16/}
}
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Yu. A. Davydov; A. L. Rozin. On sojourn times for functions and stochastic processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 3, pp. 650-654. http://geodesic.mathdoc.fr/item/TVP_1978_23_3_a16/