Self-intersection local time of fractional Brownian motions - Via chaos expansion

Kyoto Journal of Mathematics

Volumn 41, Issue 2, 2001, Pages 233-250

  Yaozhong, Hu ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041077592     PISSN: 0023608X     EISSN: None     Source Type: Journal    
DOI: 10.1215/kjm/1250517630     Document Type: Article

References (23)

1. S. Albeverio, Y. Z. Hu and X. Y. Zhou, A remark on non smoothness of self intersection local time of planar Brownian motion, Statist. Probab. Letter, 32 (1997), 57-65.
2. S. M. Berman, A central limit theorem for the renormalized self-intersection local time of a stationary process. Probability in Banach spaces, 8 (Brunswick, ME, 1991), 351-363, Progr. Probab. 30, Birkhäuser Boston, Boston, MA, 1992.
3. S. M. Berman, Self-intersections and local nondeterminism of Gaussian processes, Ann. Probab. 19-1 (1991), 160-191.
4. S. M. Berman, Local nondeterminism and local times of general stochastic processes. Ann. Inst. H. Poincaré Sect. B (N.S.) 19-2 (1983), 189-207.
5. S. M. Berman, Local nondeterminism and local times of Gaussian processes, Indiana Univ. Math. J., 23 (1973/74), 69-94.
6. S. M. Berman, Local nondeterminism and local times of Gaussian processes, Bull. Amer. Math. Soc., 79 (1973), 475-477.
7. T. E. Duncan, Y. Z. Hu and B. Pasik-Duncan, Itô calculus for fractional Brownian motions I-Theory, SIAM J. Control Optim., 38 (2000), 582-612.
8. M. De Faria, T. Hida, L. Streit and H. Watanabe, Intersection local times as generalized white noise functionals, Acta Appl. Math., 46 (1997), 351-362.
9. S. W. He, W. Q. Yang, R. Q. Yao and J. G. Wang, Local times of self-intersection for multidimensional Brownian motion, Nagoya Math. J., 138 (1995), 51-64.
10. Y. Z. Hu, On the self-intersection local time of Brownian motion - via chaos expansion, Publ. Mat., 40 (1996), 337-350.
11. Y. Z. Hu, Itô-Wiener chaos expansion with exact residual and correlation, variance inequalities, J. of Theoret. Probab., 10 (1997), 835-848.
12. Y. Z. Hu and G. Kallianpur, Exponential integrability and application to stochastic quantization, J. Appl. Math. and Optimization, 37 (1998), 295-353.
13. Y. Z. Hu and P. A. Meyer, Chaos de Wiener et intégrales de Feynman. Séminaire de Probabilités XXII, ed. by J. Azema, P. A. Meyer and M. Yor, Lecture Notes in Math. 1321, Springer, 1988, 51-71.
14. Y. Z. Hu and B. Øksendal, Chaos expansion of local time of fractional Brownian motions, preprint 2000.
15. d and renormalization, Stochastic Process. Appl., 56 (1995), 1-34.
16. P. A. Meyer, Quantum Probability for Probabilists, Lecture, Notes in Math. 1538, Springer, 1993.
17. J. Neveu, Processus Aléatoires Gaussiens. Les Presses De L'Université De Montréal, 1968.
18. D. Nualart and J. Vives, Chaos expansion and local time, Publ. Mat., 36-2 (1992), 827-836.
19. J. Rosen, The intersection local time of fractional Brownian motion in the plane, J. Multivariate Anal., 23-1 (1987), 37-46.
20. B. B. Mandelbrot and J. W. Van Ness, Fractional Brownian motions, fractional noises and applications, SIAM Rev., 10 (1968) 422-437.
21. 2 Euclidean Field Theory, Princeton University Press, Princeton, NJ., 1974.
22. S. R. S. Varadhan, Appendix to "Euclidean quantum field theory" by K. Symanzik, in "Local Quantum Theory" (R. Jost ed.), Academic, New York, 1969.
23. S. Watanabe, Stochastic Differential Equation and Malliavin Calculus. Tata institute of fundamental research, Springer, 1984.