Skew-product representations of multidimensional Dunkl Markov processes

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1. [1] J.-P. Anker, P. Bougerol and T. Jeulin. The infinite Brownian loop on a symmetric space. Rev. Mat. Iberoamericana 18 (2002) 41–97. Zbl1090.58020MR1924687
2. [2] P. Biane, P. Bougerol and N. O’Connell. Littelmann paths and Brownian paths. Duke Math. J. 130 (2005) 127–167. Zbl1161.60330MR2176549
3. [3] O. Chybiryakov. Processus de Dunkl et relation de Lamperti. PhD Thesis, University Paris 6, 2006. Zbl1094.60035
4. [4] C. F. Dunkl and Y. Xu. Orthogonal Polynomials of Several Variables. Cambridge University Press, Cambridge, 2001. Zbl0964.33001MR1827871
5. [5] S. N. Ethier and T. G. Kurtz. Markov Processes. Characterization and Convergence. Wiley, New York, 1986. Zbl0592.60049MR838085
6. [6] A. R. Galmarino. Representation of an isotropic diffusion as a skew product. Z. Wahrsch. Verw. Gebiete 1 (1962/1963) 359–378. Zbl0109.36303MR148118
7. [7] L. Gallardo and M. Yor. An absolute continuity relationship between two multidimensional Dunkl processes. Private communication, 2005. 
8. [8] L. Gallardo and M. Yor. Some new examples of Markov processes which enjoy the time-inversion property. Probab. Theory Related Fields 132 (2005) 150–162. Zbl1087.60058MR2136870
9. [9] L. Gallardo and M. Yor. A chaotic representation property of the multidimensional Dunkl processes. Ann. Probab. 34 (2006) 1530–1549. Zbl1107.60015MR2257654
10. [10] L. Gallardo and M. Yor. Some remarkable properties of the Dunkl martingales. Séminaire de Probabilités XXXIX 337–356. Lecture Notes in Math. 1874. Springer, Berlin, 2006. Zbl1128.60027MR2276903
11. [11] K. Itô and H. P. McKean Jr.Diffusion Processes and Their Sample Paths. Die Grundlehren der Mathematischen Wissenschaften, Band 125. Academic Press Inc., Publishers, New York, 1965. Zbl0285.60063MR199891
12. [12] N. Ikeda and S. Watanabe. Stochastic Differential Equations and Diffusion Processes. North-Holland Publishing Co., Amsterdam, 1981. Zbl0495.60005MR637061
13. [13] I. Karatzas and S. E. Shreve. Brownian Motion and Stochastic Calculus, 2nd edition. Springer-Verlag, New York, 1991. Zbl0734.60060MR1121940
14. [14] H. Kunita. Absolute continuity of Markov processes and generators. Nagoya Math. J. 36 (1969) 1–26. Zbl0186.51203MR250387
15. [15] S. Lawi. Towards a characterization of Markov processes enjoying the time-inversion property. J. Theoret. Probab. 21 (2008) 144–168. Zbl1141.60046MR2384476
16. [16] H. P. McKean Jr.Stochastic Integrals. Academic Press, New York, 1969. Zbl0191.46603MR247684
17. [17] E. J. Pauwels and L. C. G. Rogers. Skew-Product Decompositions of Brownian Motions. Geometry of Random Motion (Ithaca, N.Y., 1987), pp. 237–262. Contemp. Math. 73. Amer. Math. Soc., Providence, RI, 1988. Zbl0656.58034MR954643
18. [18] M. Rösler. Generalized Hermite polynomials and the heat equation for Dunkl operators. Comm. Math. Phys. 192 (1998) 519–542. Zbl0908.33005MR1620515
19. [19] M. Rösler. Dunkl operators: theory and applications. Orthogonal Polynomials and Special Functions (Leuven, 2002), pp. 93–135. Lecture Notes in Math. 1817. Springer, Berlin, 2003. Zbl1029.43001MR2022853
20. [20] M. Rösler and M. Voit. Markov processes related with Dunkl operators. Adv. in Appl. Math. 21 (1998) 575–643. Zbl0919.60072MR1652182
21. [21] D. Revuz and M. Yor. Continuous Martingales and Brownian Motion, 3rd edition. Springer-Verlag, Berlin, 1999. Zbl0917.60006MR1725357
22. [22] M. Yor. Exponential Functionals of Brownian Motion and Related Processes. Springer-Verlag, Berlin, 2001. (With an introductory chapter by Hélyette Geman, Chapters 1, 3, 4, 8 translated from the French by Stephen S. Wilson.) Zbl0999.60004MR1854494

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