Geodesic
Random mappings and a generalized additive functionals of a Wiener process
Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 1, pp. 43-61

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The definition of a generalized additive homogeneous functional of a Wiener process is introduced. It is shown that a generalized functional is uniquely specified by its characteristics. In this case the functions from the Schwartz space $S^*$ of slowly growing generalized functions play the role of generating functions.
Keywords: generalized Wiener functionals, multiple stochastic integrals, additive functionals. 
@article{TVP_2003_48_1_a2,
     author = {A. A. Dorogovtsev and V. V. Bakunin},
     title = {Random mappings and a generalized additive functionals of a {Wiener} process},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {43--61},
     publisher = {mathdoc},
     volume = {48},
     number = {1},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2003_48_1_a2/}
}
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A. A. Dorogovtsev; V. V. Bakunin. Random mappings and a generalized additive functionals of a Wiener process. Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 1, pp. 43-61. http://geodesic.mathdoc.fr/item/TVP_2003_48_1_a2/