no. 2
Upper and lower limits of doubly perturbed brownian motion
Annales de l'I.H.P. Probabilités et statistiques, Tome 36 (2000) no. 2, pp. 219-249. 
@article{AIHPB_2000__36_2_219_0,
     author = {Chaumont, L. and Doney, R. A. and Hu, Y.},
     title = {Upper and lower limits of doubly perturbed brownian motion},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {219--249},
     publisher = {Gauthier-Villars},
     volume = {36},
     number = {2},
     year = {2000},
     mrnumber = {1751659},
     zbl = {0969.60082},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPB_2000__36_2_219_0/}
}
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Chaumont, L.; Doney, R. A.; Hu, Y. Upper and lower limits of doubly perturbed brownian motion. Annales de l'I.H.P. Probabilités et statistiques, Tome 36 (2000) no. 2, pp. 219-249. http://archive.numdam.org/item/AIHPB_2000__36_2_219_0/

[1] Bingham N.N., Goldie C.M., Teugels J.L., Regular Variation, Cambridge University Press, 1987. | MR | Zbl

[2] Carmona Ph., Petit P., Yor M., Some extensions of the arc sine law as partial consequences of the scaling property for Brownian motion, Probab. Theory Related Fields 100 (1994) 1-29. | MR | Zbl

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

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

[5] Chaumont L., Doney R.A., Some calculations for doubly perturbed Brownian motion, Stoch. Proc. Appl. (1999), to appear. | MR | Zbl

[6] Csáki E., On the lower limits of maxima and minima of Wiener process and partial sums, Z. Wahrsch. Verw. Gebiete. 43 (1978) 205-221. | MR | Zbl

[7] Csáki E., An integral test for the supremum of Wiener local time, Probab. Theory Related Fields 83 (1989) 207-217. | MR | Zbl

[8] Csörgö M., Révész P., Strong Approximations in Probability and Statistics, Akadémiai Kiadó, Budapest and Academic Press, New York, 1981. | MR | Zbl

. [9] Davis B., Weak limits of perturbed Brownian motion and the equation Yt = Bt + σ sup{Ys: s ≤ t} + β inf{Ys: s ≤ t}, Ann. Probab. 24 (1996) 2007-2017. | MR | Zbl

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

[11] Doney R.A., Some calculations for perturbed Brownian motion, in: Azéma J., Émery M., Ledoux M., Yor M. (Eds.), Sém. Probab. XXXII, Lecture Notes Math., Vol. 1686, Springer, Berlin, 1998, pp. 231-236. | EuDML | Numdam | MR | Zbl

[12] Doney R.A., Warren J., Yor M., Perturbed Bessel processes, in: Azéma J., Émery M., Ledoux M., Yor M. (Eds.), Sém. Probab. XXXII, Lecture Notes Math., Vol. 1686, Springer, Berlin, 1998, pp. 237-249. | EuDML | Numdam | MR | Zbl

[13] Getoor R.K., The Brownian escape process, Ann. Probab. 7 (1979) 864-867. | MR | Zbl

[14] Jeulin Th., Ray-Knight's theorem on Brownian local times and Tanaka's formula, in: Çinlar E., Chung K.L., Getoor R.K. (Eds.), Sem. Stoch. Proc., Birkhauser, Boston, 1984, pp. 131-142. | MR | Zbl

[15] Kochen S.B., Stone C.J., A note on the Borel-Cantelli lemma, Illinois J. Math. 8 (1964) 248-251. | MR | Zbl

[16] Le Gall J.F., L'équation stochastique Yt = Bt + αMYt + βIYt comme limite des équations de Norris-Rogers-Williams, 1986, unpublished notes.

[17] Le Gall J.F., Yor M., Enlacement du mouvement brownien autour des courbes de l'espace, Trans. Amer. Math. Soc. 317 (1990) 687-722. | MR | Zbl

[18] Mcgill P., Markov properties of diffusion local times: a martingale approach, Adv. Appl. Probab. 14 (1982) 789-810. | MR | Zbl

[19] Norris J.R., Rogers L.C.G., Williams D., Self-avoiding random walk: a Brownian motion model with local time drift, Probab. Theory Related Fields 74 (1987) 271- 287. | MR | Zbl

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

[21] Petit F., Sur le temps passé par le mouvement brownien au-dessus d'un multiple de son supremum et quelques extensions de la loi de l'arc sinus, Part of a Thèse de Doctorat, Université Paris VII, 1992.

[22] Revuz D., Yor M., Continuous Martingales and Brownian Motion, 2nd edn., Springer, Berlin, 1994. | MR | Zbl

[23] Révész P., Random Walk in Random and Non-Random Environment, World Scientific Press, Singapore, London, 1990. | MR | Zbl

[24] Shi Z., Werner W., Asymptotics for occupations times of half-lines by stable processes and perturbed reflecting Brownian motion, Stochastics 55 (1995) 71-85. | MR | Zbl

[25] Tóth B., The "true" self-avoiding walk with bond repulsion in Z: limit theorems, Ann. Probab. 23 (1995) 1523-1556. | MR | Zbl

[26] Tóth B., "True" self-avoiding walk with generalized bond repulsion in Z, J. Stat. Phys. 77 (1994) 17-33. | MR | Zbl

[27] Tucker H.G., On a necessary and sufficient condition that an infinitely divisible distribution be absolutely continuous, Amer. Math. Soc. Trans. 118 (1965) 316- 330. | MR | Zbl

[28] Werner W., Some remarks on perturbed reflecting Brownian motion, in: Azéma J., Émery M., Meyer P.A., Yor M. (Eds.), Sém. Probab. XXIX, Lecture Notes Math., Vol. 1613, Springer, Berlin, 1995, pp. 37-43. | EuDML | Numdam | MR | Zbl

[29] Yor M., Some Aspects of Brownian Motion, Part I: Some Special Functionals, Lecture Notes, ETH Zürich, Birkhäuser, Basel, 1992. | MR | Zbl

[30] Yor M., Local Times and Excursions for Brownian Motion: A Concise Introduction, Lecciones en Metemáticas, Número I, Universidao Central de Venezuela, Caracas, 1995.