On the upcrossing chains of stopped brownian motion
Séminaire de probabilités de Strasbourg, Volume 32 (1998), p. 343-375
@article{SPS_1998__32__343_0,
     author = {Knight, Frank B.},
     title = {On the upcrossing chains of stopped brownian motion},
     journal = {S\'eminaire de probabilit\'es de Strasbourg},
     publisher = {Springer - Lecture Notes in Mathematics},
     volume = {32},
     year = {1998},
     pages = {343-375},
     zbl = {0917.60077},
     mrnumber = {1655304},
     language = {en},
     url = {http://www.numdam.org/item/SPS_1998__32__343_0}
}
Knight, Frank B. On the upcrossing chains of stopped brownian motion. Séminaire de probabilités de Strasbourg, Volume 32 (1998) pp. 343-375. http://www.numdam.org/item/SPS_1998__32__343_0/

1. Chacon, R., Lejan, Y., Perkins, E. and Taylor, S.J., Generalized arc length for Brownian motion and Lévy processes, Z. Wahrsch. Verw. Gebiete 57 (1981), 197-211. | MR 626815 | Zbl 0469.60037

2. Feller, W., An Introduction to Probability Theory and its Applications, Vol. I., 3rd Edition. John Wiley and Sons, New York (1968). | MR 228020 | Zbl 0155.23101

3. Knight, F.B., On the random walk and Brownian motion, TAMS 103 (1962), 218-228. | MR 139211 | Zbl 0279.60057

4. _, Random walks and a sojourn density process of Brownian motion, TAMS 109 (1963), 56-86. | MR 154337 | Zbl 0119.14604

5. _, Brownian local times and taboo processes, TAMS 143 (1969), 173-185. | MR 253424 | Zbl 0187.41203

6. _, Approximation of stopped Brownian local time by dyadic crossing chains, Stochastic Processes and their Applications Vol. 66, No 2 (1997), 253-271. | MR 1440401 | Zbl 0889.60083

7. Pitman, J., and Yor, M., A decomposition of Bessel bridges, Z. Wahrsch. Verw. Gebiete 59 (1982), 425-457. | MR 656509 | Zbl 0484.60062

8. Walsh, J.B., Downcrossings and the Markov property of local time, In Temps Locaux, Asterisque 52-53 (1978), 89-116.

9. Warren, J., and Yor, M., The Brownian burglar: conditioning Brownian motion by its local time process, Séminaire de Prob. XXXII (?). | Numdam | Zbl 0924.60072

10. Whittaker, E.T., and Watson, G.N., A Course of Modern Analysis, 4th Edition Cambridge (1965). | JFM 45.0433.02