Abstract
It is shown that diffusions with identical bridges compose classes of stochastic processes for which the methods of calculation of distributions of functionals are identical as well. Some particular classes of such processes are considered. Bibliography: 8 titles.
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REFERENCES
A. N. Borodin and P. Salminen, Handbook of Brownian Motion — Facts and Formulae, 2nd ed., Birkhäuser, Basel-Boston-Berlin (2002).
I. Benjamini and S. Lee, “Conditioned diffusions which are Brownian motions,” J. Theor. Probab., 10, 733–736 (1997).
P. J. Fitzsimmons, “Markov processes with identical bridges,” Electronic J. Probab., 3, 1–12 (1998).
M. Kac, “On distribution of certain Wiener functionals,” Trans. Amer. Math. Soc., 65, 1–13 (1949).
L. Takács, “On the generalization of the arc-sine law,” Ann. Appl. Probab., 6, 1035–1039 (1996).
P. Lévy, “Sur certains processes stochastiques homogènes,” Compositio Math., 7, 283–339 (1939).
A. N. Borodin and I. A. Ibragimov, “Limit theorems for random walks,” Trudy Mat. Inst. RAN, 195 (1994).
A. N. Borodin, “Distribution of integral functionals of the local time for random walks,” Zap. Nauchn. Semin. POMI, 177, 8–26 (1989).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 294, 2002, pp. 29–42.
This research was supported in part by the Russian Foundation for Basic Research, grants 02-01-00265, 00-15-96019, and 99-01-04027 (joint with DFG).
Translated by V. N. Sudakov.
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Borodin, A.N. Diffusion processes with identical bridges. J Math Sci 127, 1687–1695 (2005). https://doi.org/10.1007/s10958-005-0129-8
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DOI: https://doi.org/10.1007/s10958-005-0129-8