Pitman, Jim; Yor, Marc A decomposition of Bessel bridges. (English) Zbl 0484.60062 Z. Wahrscheinlichkeitstheor. Verw. Geb. 59, 425-457 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 4 ReviewsCited in 158 Documents MSC: 60J55 Local time and additive functionals 60J60 Diffusion processes 60J65 Brownian motion Keywords:Brownian local time; Bessel processes; excursion theory; Ray-Knight theorems PDFBibTeX XMLCite \textit{J. Pitman} and \textit{M. Yor}, Z. Wahrscheinlichkeitstheor. Verw. Geb. 59, 425--457 (1982; Zbl 0484.60062) Full Text: DOI References: [1] Billingsley, P., Convergence of Probability Measures (1968), New York: J. Wiley, New York · 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 (1966), New York: Wiley, New York · 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 [5] Hammersley, J. M., On the statistical loss of long-period comets from the solar system II, Proceedings of the 4^th Berkeley Symposium on Math. Statist. and Probab. Volume III, 17-78 (1960), Calif.: Astronomy and Physics. Univ., Calif. · Zbl 0114.45502 [6] Itô, K.: Poisson point processes attached to Markov processes. Proc. 6^th Berkeley Sympos. on Math. Statist and Probab. Vol. III, 225-239. Univ. Calif. (1970-1971) · Zbl 0284.60051 [7] Itô, K.; McKean, H. P., Diffusion processes and their sample paths (1965), Berlin-Heidelberg-New York: Springer, Berlin-Heidelberg-New York · Zbl 0127.09503 [8] Jeulin, Th., Semi-martingales et grossissement d’une filtration, Lect. Notes in Maths. 833 (1980), Berlin-Heidelberg-New York: Springer, Berlin-Heidelberg-New York · 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 (1981), Berlin-Heidelberg-New York: Springer, Berlin-Heidelberg-New York · Zbl 0462.60077 [10] McKean, H. P., Excursions of a non-singular diffusion, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 1, 230-239 (1963) · Zbl 0117.35903 [11] Lévy, P.: Wiener’s Random Function, and other Laplacian Random Functions. Proc. 2^nd Berkeley Sympos. Math. Statist. Probab. Vol. II, 171-186. Univ. Calif. (1950) · Zbl 0044.13802 [12] Molchanov, S., Martin boundaries for invariant Markov processes on a solvable group, Theor. Probability Appl., 12, 310-314 (1967) · Zbl 0308.60044 [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 [15] Pitman, J. W.; Rogers, L., Markov functions of Markov processes, Ann. of Probab., 9, 4, 573-582 (1981) · Zbl 0466.60070 [16] Pitman, J. W.; Yor, M.; Williams, D., Bessel processes and infinitely divisible laws, Stochastic Integrals (1981), Berlin-Heidelberg-New York: Springer, Berlin-Heidelberg-New York · Zbl 0469.60076 [17] Rogers, L., Williams characterization of the Brownian excursion law: proof and applications, Sém. Probabilité XV, 227-250 (1981), Berlin-Heidelberg-New York: Springer, Berlin-Heidelberg-New York · Zbl 0462.60078 [18] Shepp, L. A., Radon-Nikodym derivatives of Gaussian measures, Ann. Math. Statist., 37, 321-354 (1966) · Zbl 0142.13901 [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 [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 [22] Watson, G. N., A Treatise on the Theory of Bessel Functions (1966), Cambridge: University Press, Cambridge · 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 [24] Williams, D., Diffusions, Markov Processes, and Martingales. Vol. 1: Foundations (1979), New York: J. Wiley, New York · Zbl 0402.60003 [25] Williams, D., Markov properties of Brownian local time, Bull. Amer. Math. Soc., 75, 1035-1036 (1969) · Zbl 0266.60060 [26] Williams, D., Decomposing the Brownian path, Bull. Amer. Math. Soc., 76, 871-873 (1970) · Zbl 0233.60066 [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.