Perturbed Skorohod equations and perturbed reflected diffusion processes
Annales de l'I.H.P. Probabilités et statistiques, Volume 41 (2005) no. 1, p. 107-121
@article{AIHPB_2005__41_1_107_0,
     author = {Doney, Ron A. and Zhang, T.},
     title = {Perturbed Skorohod equations and perturbed reflected diffusion processes},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Elsevier},
     volume = {41},
     number = {1},
     year = {2005},
     pages = {107-121},
     doi = {10.1016/j.anihpb.2004.03.005},
     zbl = {1061.60056},
     mrnumber = {2110448},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2005__41_1_107_0}
}
Perturbed Skorohod equations and perturbed reflected diffusion processes. Annales de l'I.H.P. Probabilités et statistiques, Volume 41 (2005) no. 1, pp. 107-121. doi : 10.1016/j.anihpb.2004.03.005. http://www.numdam.org/item/AIHPB_2005__41_1_107_0/

[1] Ph. Carmona, F. Petit, M. Yor, Some extentions of the arcsine law as (partial) consequences of the scaling property of Brownian motion, Probab. Theory Related Fields 100 (1994) 1-29. | MR 1292188 | Zbl 0808.60066

[2] Ph. Carmona, F. Petit, M. Yor, Beta variables as times spent in [0,) by certain perturbed Brownian motions, J. London Math. Soc. 58 (1998) 239-256. | Zbl 0924.60067

[3] L. Chaumont, R.A. Doney, Pathwise uniqueness for perturbed versions of Brownian motion and reflected Brownian motion, Probab. Theory Related Fields 113 (1999) 519-534. | MR 1717529 | Zbl 0945.60082

[4] L. Chaumont, R.A. Doney, Some calculations for doubly perturbed Brownian motion, Stochastic Process. Appl. 85 (1) (2000) 61-74. | MR 1730618 | Zbl 0997.60095

[5] B. Davis, Weak limits of perturbed random walks and the equation Y t =B t +α sup st Y s +β inf st Y s , Ann. Probab. 24 (1996) 2007-2023. | Zbl 0870.60076

[6] B. Davis, Brownian motion and random walk perturbed at extrema, Probab. Theory Related Fields 113 (1999) 501-518. | MR 1717528 | Zbl 0930.60041

[7] R.A. Doney, Some calculations for perturbed Brownian motion, in: Seminaire de Probabilites XXXII, Lecture Notes in Mathematics, 1998, pp. 231-236. | Numdam | MR 1655296 | Zbl 0911.60067

[8] N. Ikeda, S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland/Kodansha, 1989. | MR 1011252 | Zbl 0684.60040

[9] J.F. Le Gall, M. Yor, Excursions browniennes et carrés de processus de Bessel, C. R. Acad. Sci. Paris Sér. I 303 (1986) 73-76. | MR 851079 | Zbl 0589.60070

[10] J.F. Le Gall, M. Yor, Enlacements du mouvement brownien autour des courbes de l'espace, Trans. Amer. Math. Soc. 317 (1990) 687-7722. | MR 946219 | Zbl 0696.60072

[11] P.L. Lions, A.S. Sznitman, Stochastic differential equations with reflecting boundary conditions, Comm. Pure Appl. Math. 37 (1984) 511-537. | MR 745330 | Zbl 0598.60060

[12] M. Perman, W. Werner, Perturbed Brownian motions, Probab. Theory Related Fields 108 (1997) 357-383. | MR 1465164 | Zbl 0884.60082

[13] D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer, Berlin, 1994. | MR 1303781 | Zbl 0804.60001

[14] W. Werner, Some remarks on perturbed Brownian motion, in: Seminaire de Probabilites XXIX, Lecture Notes in Mathematics, vol. 1613, 1995, pp. 37-43. | Numdam | MR 1459447 | Zbl 0835.60072

[15] T.S. Zhang, On the strong solutions of one-dimensional stochastic differential equations with reflecting boundary, Stochastic Process. Appl. 50 (1994) 135-147. | MR 1262335 | Zbl 0796.60062