Geodesic
Inverse first exit problem for Wiener process
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 2, Tome 244 (1997), pp. 302-314 Cet article a éte moissonné depuis la source Math-Net.Ru

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An inverse first exit problem for Wiener process is considered. This problem is to find such a ragion $G\colon(0,0)\in G\cup\partial G\subset R_+\times R$ that a distribution of the first exit point from it has a priory given property. For to estimate of this region with the uniform distribution of the first exit point a theorem on comparing of densities and a theorem on moment characterization are used. When the uniform density tends to zero and to infinity two asymptotics are investigated. 
@article{ZNSL_1997_244_a21,
     author = {B. P. Harlamov},
     title = {Inverse first exit problem for {Wiener} process},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {302--314},
     year = {1997},
     volume = {244},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_244_a21/}
}
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B. P. Harlamov. Inverse first exit problem for Wiener process. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 2, Tome 244 (1997), pp. 302-314. http://geodesic.mathdoc.fr/item/ZNSL_1997_244_a21/