Thèmes de recherche : PROBABILITÉS et ANALYSE HARMONIQUE sur les STRUCTURES GEOMETRIQUES.
applications dans les STATISTIQUES MULTIVARIÉES

1. Lévy-Kchinchine formula on vector spaces ( avec T.Byczkowski), IV International Conference on Probability Theory on Vector Spaces, Lancut, 1987. LNM 1391(1989), 23-32.
2. Malliavin calculus for stable processes on homogeneous groups, Studia Mathematica 100(1991), 183-205.
3. A central limit theorem on the space of positive definite symmetric matrices, Ann.Inst.Fourier 42(1992), 857-874.
4. Malliavin calculus for stable processes on Heisenberg group (avec T.Byczkowski), Prob.Math.Stat. 13(1993), 277-292.
5. Dispersions and a central limit theorem on symmetric spaces, Bull.Sciences Math. 118(1994), 1-12.
6. Cramér theorem on symmetric spaces of noncompact type, J.Theor.Prob. 7(1994), 609 - 613.
7. Bochner and Schoenberg theorems on symmetric spaces in the complex case (avec J.J.Loeb), Bull Soc. Math. France 122(1994), 571-590.
8. Spherical analysis and central limit theorems on symmetric spaces(avec J.J.Loeb), Proc. Probability Measures on Groups and Related Structures XI, Oberwolfach 1994, World Scientific, 146-166.
9. Espace de Hardy d'un espace symétrique de type hermitien, Journées "Programme de Gelfand - Gindikin" Paris 1996, Institut de Mathématiques de Jussieu.
10. Function c on an ordered symmetric space, Bull.Sciences Math.(1997), 561-572.
11. Factorization theorems on symmetric spaces of non-compact type, J.Theor.Prob. 12(1999), 375-383.
12. On the Skitovich-Darmois theorem for compact Abelian groups (avec G.M. Feldman), J.Theor.Prob. 13(2000) , 859-869.
13. Independent linear statistics on finite Abelian groups (avec G.M. Feldman), Ukr.Math.J., AMS Translations 53(2001), 499-506.
14. A Bernstein property on groups (avec J.J. Loeb), Prob.Math.Stat. 20(2000), 141-149.
15. Classical theorems of probability on Gelfand pairs - Khinchin theorems and Cramer theorem (avec C.R.E. Raja), Israel Journal of Math. 132 (2002), 61-107.
16. The product formula for the spherical functions on symmetric spaces in the complex case (avec P. Sawyer), Pacific J. Math. 204(2002), 377-393.
17. Gaussian measures as limits on irreducible symmetric spaces and cones, Contemporary Mathematics 287(2001),111-125.
18. The complex Wishart distribution and the symmetric group (avec G. Letac et H. Massam), Annals of Statistics 31(2003), 287-309.
19. The product formula for the spherical functions on symmetric spaces of non-compact type(avec P. Sawyer), J. Lie Theory 13(2003), 247-261.
20. Some convexity results for the Cartan decomposition (avec P. Sawyer), Canadian J. Math. 55(2003), 1000-1018.
21. On the Skitovich-Darmois Theorem for Discrete Abelian Groups(avec G. Feldman), Theory Prob. Appl. 49(3) (2004), 596-601.
22. Transition density estimates for stable processes on symmetric spaces (avec A. Stos), Pacific Journal of Math., 217(2004), 87-100.
23. The hyperoctahedral group, Symmetric Group Representations and the moments of the real Wishart distribution (avec G. Letac et H. Massam), J. Theor. Probability, 18(2005), 1-42.
24. A composition formula for squares of Hermite polynomials and its generalizations (avec A. Nowak), CRAS Paris, Ser.I 338(2004), 849-852.
25. Higher order Riesz Transforms, fractional derivatives, and Sobolev spaces for Laguerre expansions (avec J.J. Loeb, I. Lopez, A. Nowak, W. Urbina), Journal Math. Pures et Appl., 84(2005), 375 - 405.
26. On the kernel of the product formula on symmetric spaces (avec P. Sawyer), Journal Geom. Analysis, 14(2004), 653-672.
27. A formula for polynomials with Hermitian matrix argument, (avec C. Balderrama et W. Urbina), Bull.Sc.Math. 129(2005), 486-500.
28. Moments of Wishart Processes via Ito Calculus, (avec L. Vostrikova), Teor. Veroyatn. Primen. 51 (2006), no. 4, 732--751; translation in Theory Probab. Appl. 51 (2007), no. 4, 609--625
29. Poisson kernels of half--spaces in real hyperbolic spaces, (avec T. Byczkowski et A. Stos), Revista Mat. Iberoam.23(2007), 85-126.
30. Exit times and Poisson kernels of the Ornstein--Uhlenbeck diffusion, ( avec T. Jakubowski), Stoch. Models 24 (2008), no. 2, 314 - 337.
31. Fine structure of the complex hyperbolic Brownian Motion and Rudin's question(avec T. Zak), Prob.Math.Stat 28(2008), 345-357.
32. Semigroups associated to generalized polynomials and some classical formulas, (avec C. Balderrama et W. Urbina)J. Math. Pures Appl. 92(2009), 375-395.
33. Hypercontractivity for log-subharmonic functions, (avec J.J.Loeb et T. Kemp), J. Funct. Anal. 258(2010), 1785-1805.
34. On Wiener-Hopf factors for stable processes (avec T. Jakubowski), Annales Inst. H.Poincaré, Probabilités et Statistiques 47, No. 1, 9-19 (2011).
35. The Skitovich-Darmois Theorem for locally compact Abelian groups(avec G. Feldman), Journal of the Australian Mathematical Society 88(2010),339-352.
36. Strong Central Limit Theorem for Isotropic Random Walks in R^d (avec J.J. Loeb et T. Zak), Probab. Theory Relat. Fields 151(2011), 153--172.
37. Absolute continuity of convolutions of orbital measures on Riemannian symmetric spaces (avec P. Sawyer), Journal of Functional Analysis 259(2010), 1759-1770.
38. A sharp criterion for the existence of the product formula on symmetric spaces of type A_n (avec P. Sawyer), J.Lie Theory 20 (2010), 751-766.
39. On exit time of stable processes, (avec T. Jakubowski), Stochastic Processes and their Applications Volume 122, Issue 1, January 2012, p.31-41.
40. Analysis of Ornstein--Uhlenbeck and Laguerre Stochastic Processes (avec T. Jakubowski), in " Orthogonal Families and Semigroups in Analysis and Probability", P. Graczyk and W. Urbina, editors, Seminaires et Congres 25, Editions SMF, Paris, 2012.
41. Hitting half-spaces or spheres by the Ornstein-Uhlenbeck type diffusions, (avec T. Byczkowski, J. Chorowski, J. Malecki), Colloq. Math. 129 (2012), p. 145-171
42. Multidimensional Yamada-Watanabe theorem and its applications to particle systems (avec J. Malecki), Journal of Mathematical Physics, 54 (2013), pp. 021503-021503-15.
43. Martin representation, Relative Fatou Theorem and Hardy spaces for fractional Laplacian with a gradient perturbation (avec T. Jakubowski et T. Luks), Positivity 17 (2013), 1043-1070.
44. On the product formula on noncompact Grassmannians (avec P. Sawyer), Coll.Math. 133 (2013), 145-167.
45. Riesz measures and Wishart laws associated to quadratic maps (avec H. Ishi), Journal of Jap.Math.Soc.66(2014), 317-348.
46. On a functional equation appearing in characterization of distributions by the optimality of an estimate(avec G. Feldman), Aequat. Math.,89(2015), pp 663-67. DOI 10.1007/S00010-014-0254-x.
47. Strong Logarithmic Sobolev Inequalities for log-subharmonic functions (avec J.J.Loeb et T. Kemp), Canadian J. Math. 67(2015), 1384-1410.
48. Fisher Information of Exponential Families Parametrized by a Segment of Means (avec S. Mamane), Probab.Math.Statistics 35(2015), 73?90.
49. Stochastic Analysis Methods in Wishart Theory I, in: Modern Methods of Multivariate Statistics, P. Graczyk, A. Hassairi Eds., Travaux en Cours 82, Hermann, Paris, 2014.
50. Convolution of orbital measures on symmetric spaces of type C_p and D_p (avec P. Sawyer), J. Aust. Math. Soc.98 (2015), 232-256 doi:10.1017/S1446788714000494
51. Strong solutions of non-colliding particle systems(avec J. Malecki), Electron. J. Probab.,19(2014), no. 119, 1-21, doi 10.1214/EJP.v19-3842.
52. Convolution of orbital measures on symmetric spaces: a survey(avec P. Sawyer),to appear in Contemporary Mathematics AMS, 2016.
53. On inversions and Doob h-transforms of linear diffusions(avec L. Alili et T. Zak), In Memoriam Marc Yor, Séminaire de Probabilités XLVII, Springer Lecture Notes in Math. Vol. 2137 (2015).


Submitted



54. Inversion, duality and Doob h-transforms for self-similar Markov processes (avec L. Alili, L. Chaumont, and T. Zak), 2016.


In preparation



55. On conjectures on Gindikin sets (avec J. Malecki, E. Mayerhofer), 2016.
56. Generalized Squared Bessel particle systems(avec J. Malecki), preprint, 2016.
57. L.~Alili, L.~Chaumont, P.~Graczyk and T.~\.Zak, Inversions and Kelvin transform for multidimensional self-similar Markov processes. preprint, 2016.
58. Riesz and Wishart distributions on the cones related to $A_n$ graphs (avec H. Ishi , S. Mamane), preprint, 2016.
59. Potential theory of Dunkl processes of rank 1(avec M. Roesler et T. Luks), preprint, 2016.
60. On Letac-Massam Conjecture on cones $Q_{A_n}$, (avec H. Ishi, S. Mamane, H. Ochiai), preprint, 2016.
61. Variance function of Wishart exponential families on homogeneous cones(avec H. Ishi, B. Kolodziejek), preprint, 2016.
62. Integral kernels for symmetric spaces in complex case with application to Dyson Brownian Motion (avec P. Sawyer), preprint, 2016.
63. All Wishart processes on the cone $Sym^+(n,R)$ (avec C. Pacheco, G.Uribe Bravo), preprint, 2016.