On the excursion process of Brownian motion
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- by Frank B. Knight PDF
- Trans. Amer. Math. Soc. 258 (1980), 77-86 Request permission
Abstract:
Let $W_0^ + (t)$ denote the scaled excursion process of Brownian motion, and let $l_0^ + (a), 0 \leqslant a,$ be its local time at a. The joint distribution of $l_0^ + (a), \beta (a),$ and $\gamma (a)$ is obtained, where $\beta (a)$ and $\gamma (a)$ are the last exit time and the first passage time of a by $W_0^{ + } (t)$.References
- Kai Lai Chung, Excursions in Brownian motion, Ark. Mat. 14 (1976), no. 2, 155–177. MR 467948, DOI 10.1007/BF02385832
- J. L. Doob, Heuristic approach to the Kolmogorov-Smirnov theorems, Ann. Math. Statistics 20 (1949), 393–403. MR 30732, DOI 10.1214/aoms/1177729991
- Richard T. Durrett and Donald L. Iglehart, Functionals of Brownian meander and Brownian excursion, Ann. Probability 5 (1977), no. 1, 130–135. MR 436354, DOI 10.1214/aop/1176995896
- Richard T. Durrett, Donald L. Iglehart, and Douglas R. Miller, Weak convergence to Brownian meander and Brownian excursion, Ann. Probability 5 (1977), no. 1, 117–129. MR 436353, DOI 10.1214/aop/1176995895
- William Feller, An introduction to probability theory and its applications. Vol. II, John Wiley & Sons, Inc., New York-London-Sydney, 1966. MR 0210154
- R. K. Getoor and M. J. Sharpe, Excursions of Brownian motion and Bessel processes, Z. Wahrsch. Verw. Gebiete 47 (1979), no. 1, 83–106. MR 521534, DOI 10.1007/BF00533253 K. Ito and H. P. McKean, Jr., Diffusion processes and their sample paths, Springer, Berlin, 1965.
- H. P. McKean Jr., Excursions of a non-singular diffusion, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 1 (1962/63), 230–239. MR 162282, DOI 10.1007/BF00532494
- Frank B. Knight, Brownian local times and taboo processes, Trans. Amer. Math. Soc. 143 (1969), 173–185. MR 253424, DOI 10.1090/S0002-9947-1969-0253424-7
- Frank B. Knight, On the sojourn times of killed Brownian motion, Séminaire de Probabilités, XII (Univ. Strasbourg, Strasbourg, 1976/1977) Lecture Notes in Math., vol. 649, Springer, Berlin, 1978, pp. 428–445. MR 520018
- Paul Lévy, Sur certains processus stochastiques homogènes, Compositio Math. 7 (1939), 283–339 (French). MR 919
- Douglas P. Kennedy, The distribution of the maximum Brownian excursion, J. Appl. Probability 13 (1976), no. 2, 371–376. MR 402955, DOI 10.1017/s0021900200094468
- G. E. Roberts and H. Kaufman, Table of Laplace transforms, W. B. Saunders Co., Philadelphia-London, 1966. MR 0190638
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 258 (1980), 77-86
- MSC: Primary 60J65; Secondary 60J55
- DOI: https://doi.org/10.1090/S0002-9947-1980-0554319-6
- MathSciNet review: 554319