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A decomposition of Bessel bridges. (English) Zbl 0484.60062

MSC:
60J55 Local time and additive functionals
60J60 Diffusion processes
60J65 Brownian motion
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[1] Billingsley, P.: Convergence of Probability Measures. New York: J. Wiley 1968 · Zbl 0172.21201
[2] Doob, J.L.: Conditional Brownian motion and the boundary limits of harmonic functions. Bull. Soc. Math. France 85, 431-458 (1957) · Zbl 0097.34004
[3] Feller, W.: An Introduction to Probability Theory and its Applications, vol. II. New York: Wiley 1966 · Zbl 0138.10207
[4] Getoor, R.K., Sharpe, M.J.: Excursions of Brownian motion and Bessel processes. Z. Wahrscheinlichkeitstheorie verw. Gebiete 47, 83-106 (1979) · Zbl 0399.60074 · doi:10.1007/BF00533253
[5] Hammersley, J.M.: On the statistical loss of long-period comets from the solar system II. Proceedings of the 4th Berkeley Symposium on Math. Statist. and Probab. Volume III, 17-78. Astronomy and Physics. Univ. Calif. (1960)
[6] Itô, K.: Poisson point processes attached to Markov processes. Proc. 6th Berkeley Sympos. on Math. Statist and Probab. Vol. III, 225-239. Univ. Calif. (1970-1971)
[7] Itô, K., McKean, H.P.: Diffusion processes and their sample paths. Berlin-Heidelberg-New York: Springer 1965 · Zbl 0127.09503
[8] Jeulin, Th.: Semi-martingales et grossissement d’une filtration. Lect. Notes in Maths. 833. Berlin-Heidelberg-New York: Springer 1980 · Zbl 0444.60002
[9] Jeulin, Th., Yor, M.: Sur les distributions de certaines fonctionnelles du mouvement brownien. Sém. Probas XV. Lect. Notes in Math. 850. Berlin-Heidelberg-New York: Springer 1981 · Zbl 0462.60077
[10] McKean, H.P.: Excursions of a non-singular diffusion. Z. Wahrscheinlichkeitstheorie verw. Gebiete 1, 230-239 (1963) · Zbl 0117.35903 · doi:10.1007/BF00532494
[11] Lévy, P.: Wiener’s Random Function, and other Laplacian Random Functions. Proc. 2nd Berkeley Sympos. Math. Statist. Probab. Vol. II, 171-186. Univ. Calif. (1950)
[12] Molchanov, S.: Martin boundaries for invariant Markov processes on a solvable group. Theor. Probability Appl. 12, 310-314 (1967) · Zbl 0292.60119 · doi:10.1137/1112036
[13] Petiau, G.: La théorie des fonctions de Bessel. C.N.R.S. (1955) · Zbl 0067.04704
[14] Pitman, J.W.: One-dimensional Brownian motion and the three-dimensional Bessel process. Adv. Appl. Probab. 7, 511-526 (1975) · Zbl 0332.60055 · doi:10.2307/1426125
[15] Pitman, J.W., Rogers, L.: Markov functions of Markov processes. Ann. of Probab. 9, 4, 573-582 (1981) · Zbl 0466.60070 · doi:10.1214/aop/1176994363
[16] Pitman, J.W., Yor, M.: Bessel processes and infinitely divisible laws, in: ?Stochastic Integrals?, ed. D. Williams. Lect Notes in Mathematics no. 851. Berlin-Heidelberg-New York: Springer 1981 · Zbl 0469.60076
[17] Rogers, L.: Williams characterization of the Brownian excursion law: proof and applications. Sém. Probabilité XV. Lect. Notes in Maths. 850, 227-250. Berlin-Heidelberg-New York: Springer 1981
[18] Shepp, L.A.: Radon-Nikodym derivatives of Gaussian measures. Ann. Math. Statist. 37, 321-354 (1966) · Zbl 0142.13901 · doi:10.1214/aoms/1177699516
[19] Shiga, T., Watanabe, S.: Bessel diffusions as a one-parameter family of diffusion processes, Z. Wahrscheinlichkeitstheorie verw. Gebiete 27, 37-46 (1973) · Zbl 0327.60047 · doi:10.1007/BF00736006
[20] Walsh, J.: Excursions and Local Time. Astérisque 52-53, 159-192 (1978)
[21] Watanabe, S.: On time inversion of one-dimensional diffusion processes. Z. Wahrscheinlichkeitstheorie verw. Gebiete 31, 115-124 (1975) · Zbl 0286.60035 · doi:10.1007/BF00539436
[22] Watson, G.N.: A Treatise on the Theory of Bessel Functions. Cambridge: University Press 1966 · Zbl 0174.36202
[23] Williams, D.: Path decomposition and continuity of local time for one-dimensional diffusions, I. Proc. London Math. Soc. Ser. 3, 28, 738-768 (1974) · Zbl 0326.60093 · doi:10.1112/plms/s3-28.4.738
[24] Williams, D.: Diffusions, Markov Processes, and Martingales. Vol. 1: Foundations. New York: J. Wiley 1979 · Zbl 0402.60003
[25] Williams, D.: Markov properties of Brownian local time. Bull. Amer. Math. Soc. 75, 1035-1036 (1969) · Zbl 0266.60060 · doi:10.1090/S0002-9904-1969-12350-5
[26] Williams, D.: Decomposing the Brownian path. Bull. Amer. Math. Soc. 76, 871-873 (1970) · Zbl 0233.60066 · doi:10.1090/S0002-9904-1970-12591-5
[27] Yamada, T., Watanabe, S.: On the uniqueness of solutions of stochastic differential equations. J. Math. Kyoto Univ., 11, no. 1, 155-167 (1971) · Zbl 0236.60037
[28] Yor, M.: Loi de l’indice du lacet brownien, et distribution de Hartman-Watson. Z. Wahrscheinlichkeitstheorie verw. Gebiete 53, 71-95 (1980) · Zbl 0436.60057 · doi:10.1007/BF00531612
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