From Tanaka's formula to Ito's formula : distributions, tensor products and local times
Rajeev, Bhaskaran
Séminaire de probabilités de Strasbourg, Tome 35 (2001), p. 371-389 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 2001-01-01
@article{SPS_2001__35__371_0,
     author = {Rajeev, Bhaskaran},
     title = {From Tanaka's formula to Ito's formula : distributions, tensor products and local times},
     journal = {S\'eminaire de probabilit\'es de Strasbourg},
     volume = {35},
     year = {2001},
     pages = {371-389},
     mrnumber = {1837298},
     zbl = {0979.60030},
     language = {en},
     url = {http://dml.mathdoc.fr/item/SPS_2001__35__371_0}
}

Rajeev, Bhaskaran. From Tanaka's formula to Ito's formula : distributions, tensor products and local times. Séminaire de probabilités de Strasbourg, Tome 35 (2001) pp. 371-389. http://gdmltest.u-ga.fr/item/SPS_2001__35__371_0/

1. Bass, R. (1984) : Joint continuity and representations of additive functionals of d dimensional Brownian motion, Stoch. Proc. Appl. 17 (1984), 211-227. | MR 751203 | Zbl 0543.60080

2. Bertoin, J. (1990) : Complements on Hilbert transform and the fractional derivative of Brownian motion, Journal of Mathematics of Kyoto University 30, 4(1990). | MR 1088348 | Zbl 0725.60084

3. Biane Ph., Yor, M. (1987) : Valeurs principales associées aux temps locaux brownien, Bul. Sci. Math. 111, 23-101. | MR 886959 | Zbl 0619.60072

4. Boufoussi B., Roynette B. (1993) : Le temps local brownien appartient p.s. à l'espace de Besov B1/2p,∞ , C. R. Acad. Sci., Paris, Ser. I, Math. 316. | MR 1218273 | Zbl 0788.46035

5. Brosamler, G. (1970) : Quadratic variation of potentials and harmonic functions, Transactions of the American Math. Society 147. | MR 270442 | Zbl 0248.60057

6. Dynkin, E.B. (1994) : An Introduction to Branching Measure Valued Processes, CRM Monograph series, Vol. 6, AMS Provence. | MR 1280712 | Zbl 0824.60001

7. Föllmer, H., Protter, P., Shiryaev, A.N. (1995) : Quadratic covariation and an extension of Ito's formula, Bernoulli 1/2, p. 149-169. | MR 1354459 | Zbl 0851.60048

8. Fukushima, M., Oshima Y., Takecha M. : Dirichlet forms and Symmetric Markov Processes, De Gruyter Studies in Mathematics, 19.

9. Gelfand, I., Vilenkin, N. Ya (1964) : Generalized functions Vol. 4, Academic Press, New York. | MR 173945

10. Hida, T. (1980) : Brownian Motion, Springer Verlag. | MR 562914 | Zbl 0432.60002

11. Ito, K. (1984) : Foundations of stochastic differential equations in infinite dimensional spaces, Proceedings of CBMS - NSF National Conference series in Applied Mathematics, SIAM. | MR 771478 | Zbl 0547.60064

12. Kallianpur, G., Xiong, J. (1995) : Stochastic Differential Equations in Infinite Dimensional Spaces, Lecture Notes, Monograph series, Vol. 26, Institute of Mathematical Statistics. | MR 1465436 | Zbl 0859.60050

13. Korezlioglu, H.,Ustunel, A.S. (Eds.) (1986) : Stochastic Analysis & Related Topics. Proceedings, Silvri 1986, LNM 1316, Springer Verlag. | Zbl 0634.00016

14. Krylov, N.V. (1980) : Controlled Diffusion Processes, Springer Verlag. | MR 601776 | Zbl 0459.93002

15. Le Gall, J.F. (1985) : Sur le temps local d'intersection du mouvement brownien plan et la méthode de renormalisation de Varadhan, Séminaire de Probabilités XIX, LNM 1123, Springer Verlag. | Numdam | MR 889492 | Zbl 0563.60072

16. Le Gall, J.F. (1996) : Super processes, Brownian snakes and partial differential equations, Prépublication n° 337 du Laboratoire de Probabilités de l'Université Paris VI.

17. Marcus, M.B. & Rosen, J. : Renormalised self intersection local times and Wick power chaos processes (pre-print).

18. Métivier, M., Pellaumail, J. (1969) : Stochastic Integration, Academic Press, New York.

19. Métivier, M. (1982) : Semi Martingales - A Course on Stochastic Processes, Walter de Gruyter.

20. Motoo, M. : Distribution valued additive functionals and representation of additive functionals (pre-print).

21. Meyer, P.A. (1978) : La formule d'Ito pour le mouvement brownien, d'apres G. Brosamler, Séminaire de Probabilités XII, LNM 649, Springer Verlag. | Numdam | MR 520044 | Zbl 0388.60055

22. Nualart, D. & Vives, J. (1992) : Potential Analysis No. 3, 257-263. | Zbl 0776.60092

23. Parthasarathy, K.R. (1992) : An Introduction to Quantum Stochastic Calculus, Birkhäuser. | MR 1164866 | Zbl 0751.60046

24. Protter, P. & San Martin, Jaime (1993) : General change of variable formula for semi-martingales in one and finite dimensions, Probability Theory and Related Fields 97. | Zbl 0792.60045

25. Rajeev, B. (1997) : From Tanaka formula to Ito formula : The fundamental theorem of stochastic calculus, Proceedings of the Indian Academy of Sciences (Math. Sci.), Vol. 107, No. 3, p. 319-327. | MR 1467435 | Zbl 0907.60051

26. Revuz, D., Yor, M. (1991) : Continuous Martingales and Brownian Motion, Springer Verlag. | MR 1083357 | Zbl 0731.60002

27. Röckner, M. (1993) : General Theory of Dirichlet Forms and Applications, LNM 1563, Springer Verlag, Berlin. | MR 1292279 | Zbl 0815.60075

28. Symanzik, K. (1969) : Euclidean Quantum Field Theory, In 'Local Quantum Theory', Jost. R., (Ed.)Academic Press, New York.

29. Thangavelu, S.(1993) : Lectures on Hermite and Laguerre Expansions, Princeton University Press. | MR 1215939 | Zbl 0791.41030

30. Trèves, F. (1967) : Topological Vector Spaces, Distributions and Kernels, Academic Press, New York. | MR 225131 | Zbl 0171.10402

31. Varadhan, S.R.S. (1969) : Appendix to Symanzik K. (1969) : Euclidean Quantum Field Theory, In 'Local Quantum Theory, Jost, R. (Ed.), Academic Press, New York.

32. Walsh, J.B. (1986) : An introduction to stochastic partial differential equations LNM 1180, Springer Verlag. | MR 876085 | Zbl 0608.60060

33. Watanabe, S. (1984) : Stochastic Differential Equations and Malliavin Calculus, TIFR lecture notes, Springer Verlag. | Zbl 0546.60054

34. Yor, M. (1982) : Sur la transformée de Hilbert des temps locaux browniens et une extension de la formule d'Ito, Séminaire de Probabilités, LNM 920, Springer Verlag. | Numdam | MR 658687 | Zbl 0495.60080

35. Yor, M. (1974) : Existence et unicité de diffusions à valeurs dans un espace de Hilbert, Ann. Inst. Henri Poincaré, Vol. X, no.1, p. 55 - 88. | Numdam | MR 356257 | Zbl 0281.60094

36. Da Prato, G. & Zabczyk, J. (1992) : Stochastic equations in infinite dimensions, Encyclopedia of Mathematics and its Applications 44, Cambridge University Press. | Zbl 0761.60052

37. Gawarecki, L., Mandrekar, V., & Richard, P. (1999): Existence of weak solutions for stochastic differential equations and martingale solutions for stochastic semilinear equations, Random Operators and Stochastic Equations, 7, no.3, p. 215-240. | Zbl 0951.60063

38. Kallianpur, G., Mitoma, I., & Wolpert, R.L. (1990): Diffusion equations in dual of nuclear spaces, Stochastics and Stochastics Reports, 29, p. 285-329. | Zbl 0702.60056

39. Krylov, N.V. & Rozovskii, B.L. (1981): Stochastic evolution equations, J. of Soviet Math., 16, p. 1223-1277. | Zbl 0462.60060

40. Pardoux, E. (1979): Stochastic partial differential equations and filtering of diffusion processes, Stochastics, Vol. 3, p. 127-167. | MR 553909 | Zbl 0424.60067

41. Rozovskii, B.L. (1990): Stochastic Evolution Systems, Kluwer Academic Publishers, The Netherlands. | MR 1135324 | Zbl 0724.60070