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References

  1. Ash, Robert B. Probability and measure theory. Second edition. With contributions by Catherine Doléans-Dade. Harcourt/Academic Press, Burlington, MA, 2000. xii+516 pp. ISBN: 0-12-065202-1 MR1810041 (2001j:28001)
  2. Azéma, J.; Jeulin, T.; Knight, F.; Yor, M. Quelques calculs de compensateurs impliquant l'injectivité de certains processus croissants. (French) [Some compensator calculations implying the injectivity of certain increasing processes] Séminaire de Probabilités, XXXII, 316--327, Lecture Notes in Math., 1686, Springer, Berlin, 1998. MR1655302 (2000b:60090)
  3. Bouleau, Nicolas; Yor, Marc. Sur la variation quadratique des temps locaux de certaines semimartingales. (French) C. R. Acad. Sci. Paris Sér. I Math. 292 (1981), no. 9, 491--494. MR0612544 (82d:60143)
  4. Chung, K. L.; Williams, R. J. Introduction to stochastic integration. Second edition. Probability and its Applications. Birkhäuser Boston, Inc., Boston, MA, 1990. xvi+276 pp. ISBN: 0-8176-3386-3 MR1102676 (92d:60057)
  5. Eisenbaum, Nathalie. Integration with respect to local time. Potential Anal. 13 (2000), no. 4, 303--328. MR1804175 (2002e:60085)
  6. N. Eisenbaum, Local time-space calculus for revisible semimartingales, Seminaire de Probabilites , Vol XL, Lecture Notes in Mathematics 1899, Springer-Verlag, (2007),137-146.
  7. K. D. Elworthy, A. Truman and H. Z. Zhao, Generalized Ito Formulae and space-time Lebesgue-Stieltjes integrals of local times, Seminaire de Probabilites, Vol XL, Lecture Notes in Mathematics 1899, Springer-Verlag, (2007),117-136.
  8. K. D. Elworthy, A. Truman and H. Z. Zhao, Asymptotics of Heat Equations with Caustics in One-Dimension, Preprint (2006).
  9. Feng, Chunrong; Zhao, Huaizhong. Two-parameter $p,q$-variation paths and integrations of local times. Potential Anal. 25 (2006), no. 2, 165--204. MR2238942
  10. C. R. Feng and H. Z. Zhao, Rough Path Integral of Local Time, C.R.Acad, Sci. Paris, Ser.I Math (to appear).
  11. Flandoli, Franco; Russo, Francesco; Wolf, Jochen. Some SDEs with distributional drift. II. Lyons-Zheng structure, Itô's formula and semimartingale characterization. Random Oper. Stochastic Equations 12 (2004), no. 2, 145--184. MR2065168 (2006a:60105)
  12. Föllmer, Hans; Protter, Philip; Shiryayev, Albert N. Quadratic covariation and an extension of Itô's formula. Bernoulli 1 (1995), no. 1-2, 149--169. MR1354459 (96k:60121)
  13. Föllmer, Hans; Protter, Philip. On Itô's formula for multidimensional Brownian motion. Probab. Theory Related Fields 116 (2000), no. 1, 1--20. MR1736587 (2001b:60097)
  14. Ghomrasni, R.; Peskir, G. Local time-space calculus and extensions of Itô's formula. High dimensional probability, III (Sandjberg, 2002), 177--192, Progr. Probab., 55, Birkhäuser, Basel, 2003. MR2033888 (2005j:60106)
  15. Ikeda, Nobuyuki; Watanabe, Shinzo. Stochastic differential equations and diffusion processes. North-Holland Mathematical Library, 24. North-Holland Publishing Co., Amsterdam-New York; Kodansha, Ltd., Tokyo, 1981. xiv+464 pp. ISBN: 0-444-86172-6 MR0637061 (84b:60080)
  16. Karatzas, Ioannis; Shreve, Steven E. Brownian motion and stochastic calculus. Second edition. Graduate Texts in Mathematics, 113. Springer-Verlag, New York, 1991. xxiv+470 pp. ISBN: 0-387-97655-8 MR1121940 (92h:60127)
  17. Kunita, Hiroshi. Stochastic flows and stochastic differential equations. Cambridge Studies in Advanced Mathematics, 24. Cambridge University Press, Cambridge, 1990. xiv+346 pp. ISBN: 0-521-35050-6 MR1070361 (91m:60107)
  18. Lyons, Terry; Qian, Zhongmin. System control and rough paths. Oxford Mathematical Monographs. Oxford Science Publications. Oxford University Press, Oxford, 2002. x+216 pp. ISBN: 0-19-850648-1 MR2036784 (2005f:93001)
  19. Lyons, Terence J.; Zheng, Wei An. A crossing estimate for the canonical process on a Dirichlet space and a tightness result. Colloque Paul Lévy sur les Processus Stochastiques (Palaiseau, 1987). Astérisque No. 157-158 (1988), 249--271. MR0976222 (90a:60103)
  20. McShane, Edward James. Integration. Princeton University Press, Princeton, N. J., 1944, 1957. viii+394 pp. (Fourth printing 1957). MR0082536 (18,567a)
  21. Meyer, P. A. Un cours sur les intégrales stochastiques. (French) Séminaire de Probabilités, X (Seconde partie: Théorie des intégrales stochastiques, Univ. Strasbourg, Strasbourg, année universitaire 1974/1975), pp. 245--400. Lecture Notes in Math., Vol. 511, Springer, Berlin, 1976. MR0501332 (58 #18721)
  22. Moret, S.; Nualart, D. Generalization of Itô's formula for smooth nondegenerate martingales. Stochastic Process. Appl. 91 (2001), no. 1, 115--149. MR1807366 (2002b:60097)
  23. Peskir, Goran. A change-of-variable formula with local time on curves. J. Theoret. Probab. 18 (2005), no. 3, 499--535. MR2167640 (2006k:60096)
  24. G. Peskir, A change-of-variable formula with local time on surfaces, Seminaire de Probabilites, Vol XL, Lecture Notes in Mathematics 1899, Springer-Verlag, (2007), 69-96.
  25. Peskir, Goran. On the American option problem. Math. Finance 15 (2005), no. 1, 169--181. MR2116800 (2005i:91066)
  26. Revuz, Daniel; Yor, Marc. Continuous martingales and Brownian motion. Second edition. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 293. Springer-Verlag, Berlin, 1994. xii+560 pp. ISBN: 3-540-57622-3 MR1303781 (95h:60072)
  27. Rogers, L. C. G.; Walsh, J. B. Local time and stochastic area integrals. Ann. Probab. 19 (1991), no. 2, 457--482. MR1106270 (92g:60107)
  28. Rogers, L. C. G.; Williams, David. Diffusions, Markov processes, and martingales. Vol. 2. Itô calculus. Reprint of the second (1994) edition. Cambridge Mathematical Library. Cambridge University Press, Cambridge, 2000. xiv+480 pp. ISBN: 0-521-77593-0 MR1780932 (2001g:60189)
  29. Russo, F.; Vallois, P. Itô formula for $C\sp 1$-functions of semimartingales. Probab. Theory Related Fields 104 (1996), no. 1, 27--41. MR1367665 (96m:60125)
  30. Tanaka, Hiroshi. Note on continuous additive functionals of the $1$-dimensional Brownian path. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 1 1962/1963 251--257. MR0169307 (29 #6559)
  31. Walsh, John B. An introduction to stochastic partial differential equations. École d'été de probabilités de Saint-Flour, XIV---1984, 265--439, Lecture Notes in Math., 1180, Springer, Berlin, 1986. MR0876085 (88a:60114)
  32. Wang, Albert T. Generalized Ito's formula and additive functionals of Brownian motion. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 41 (1977/78), no. 2, 153--159. MR0488327 (58 #7876)


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