Principal values of the integral functionals of brownian motion : existence continuity and an extension of Itô's formula

 Access to full text

 Full (PDF)

1. [1] Ph. Biane, M. Yor. Valeurs principales associées aux temps locaux browniens.// Bull. Sci. Math.111 (1987), p. 23-101. Zbl0619.60072MR886959
2. [2] N. Bouleau, M. Yor. Sur la variation quadratique des temps locaux de certaines semi-martingales.// C. R. Acad. Sci.Paris, Série I, 292 (1981), p. 491-494. Zbl0476.60046MR612544
3. [3] H.J. Engelbert, W. Schmidt. On the behaviour of certain functionals of the Wiener process and applications to stochastic differential equations.// Lecture Notes in Control and Information Sciences, 36 (1981), p. 47-55. Zbl0468.60077MR653645
4. [4] P.J. Fitzsimmons, J.W. Pitman, M. Yor. Markovian Bridges: construction, Palm interpretation and splicing.// Seminar on Stochastic Processes, 1992. Birkhäuser, 1993, p. 101-134. Zbl0844.60054MR1278079
5. [5] H. Föllmer, Ph. Protter, A.N. Shiryaev. Quadratic covariation and an extension of Itô's formula.// Bernoulli, 1 (1995), No. 1/2, p. 149-170. Zbl0851.60048MR1354459
6. [6] M. Fukushima, Y. Oshima, M. Takeda. Dirichlet forms and symmetric Markov processes. Walter de Gruyter, 1994. Zbl0838.31001MR1303354
7. [7] Y. Hu. The laws of Chung and Hirsch for Cauchy's principal values related to Brownian local times.// Electronic Journal of Probability, 5 (2000), No. 10, p. 1-16. Zbl0951.60079MR1768844
8. [8] Y. Hu, Z. Shi. An iterated logarithm law for Cauchy's principal value of Brownian local times.// Exponential functionals and principal values related to Brownian motion. Part B. Biblioteca de la Revista Matemática Iberoamericana, 1997. Zbl0911.60056MR1648661
9. [9] K. Itô, H.P. McKean. Diffusion processes and their sample paths. Springer, 1965. Zbl0127.09503
10. [10] J. Jacod, A.N. Shiryaev. Limit theorems for stochastic processes. Springer, 1987. Zbl0635.60021MR959133
11. [11] T. Jeulin. Application de la théorie du grossissement à l'étude des temps locaux browniens.// Lecture Notes in Mathematics, 1118 (1985), p. 197-304. Zbl0562.60080
12. [12] T. Jeulin, M. Yor. Inégalité de Hardy, semimartingales et faux-amis.// Lecture Notes in Mathematics, 721 (1979), p. 332-359. Zbl0419.60049MR544805
13. [13] T. Jeulin, M. Yor. Filtration des ponts browniens et équations différentielles stochastiques linéaires./ / Lecture Notes in Mathematics, 1426 (1989), p. 227-265. Zbl0699.60075MR1071543
14. [14] O. Kallenberg. Foundations of modern probability. Springer, 1997. Zbl0892.60001MR1464694
15. [15] R.S. Liptser, A.N. Shiryaev. Statistics of random processes, I and II. Springer, 1977 and 1978. Zbl0364.60004
16. [16] Y. Oshima, T. Yamada. On some representations of continuous additive functionals of locally zero energy.// J. Math. Soc. Japan, 36 (1984), No. 2, p. 315-339. Zbl0542.60078MR740320
17. [17] J.W. Pitman, M. Yor. A decomposition of Bessel Bridges.// Z.W.59 (1982), p. 425-457. Zbl0484.60062MR656509
18. [18] D. Revuz, M. Yor. Continuous martingales and Brownian motion. Springer, 1994. Zbl0804.60001MR1303781
19. [19] A.N. Shiryaev. Optimal stopping rules. Springer, 1978. Zbl0391.60002
20. [20] A.N. Shiryaev. Essentials of stochastic finance. World Scientific, 1998. Zbl0926.62100MR1695318
21. [21] T. Yamada. Principal values of Brownian local times and their related topics.// Itô's stochastic calculus and probability theory. Springer, 1996, p. 413-422. Zbl0878.60049MR1439540
22. [22] M. Yor. Loi de l'indice du lacet brownien et distribution de Hartman-Watson.// Z.W.53 (1980), p. 71-95. Zbl0436.60057MR576898
23. [23] M. Yor. Sur la transformée de Hilbert des temps locaux browniens et une extension de la formule d'Itô.// Lecture Notes in Mathematics, 920 (1982), p. 238-247. Zbl0495.60080MR658687
24. [24] M. Yor. On some exponential functionals of Brownian motion.// Advances in Applied Probability, 24 (1992), No. 3, p. 509-531. Zbl0765.60084MR1174378
25. [25] M. Yor. Some aspects of Brownian motion. Part II: Some recent martingale problems. Birkhäuser, 1997. Zbl0880.60082MR1442263