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@article{THSP_2011_17_2_a3, author = {V. Knopova}, title = {Asymptotic behaviour of the distribution density of some {L\'evy} functionals in $\mathbb{ R}^n$}, journal = {Teori\^a slu\v{c}ajnyh processov}, pages = {35--54}, publisher = {mathdoc}, volume = {17}, number = {2}, year = {2011}, language = {en}, url = {http://geodesic.mathdoc.fr/item/THSP_2011_17_2_a3/} }
TY - JOUR AU - V. Knopova TI - Asymptotic behaviour of the distribution density of some L\'evy functionals in $\mathbb{ R}^n$ JO - Teoriâ slučajnyh processov PY - 2011 SP - 35 EP - 54 VL - 17 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/THSP_2011_17_2_a3/ LA - en ID - THSP_2011_17_2_a3 ER -
V. Knopova. Asymptotic behaviour of the distribution density of some L\'evy functionals in $\mathbb{ R}^n$. Teoriâ slučajnyh processov, Tome 17 (2011) no. 2, pp. 35-54. http://geodesic.mathdoc.fr/item/THSP_2011_17_2_a3/
[1] M. T. Barlow, R. B. Bass, Z.-Q. Chen, M. Kassmann, “Non-local Dirichlet forms and symmetric jump processes”, Trans. Amer. Math. Soc., 361 (2009), 1963–1999
[2] M. T. Barlow, A. Grigoryan, T. Kumagai, “Heat kernel upper bounds for jump processes and the first exit time”, J. Reine Angew. Math., 626 (2009), 135–157
[3] R. F. Bass, D. A. Levin, “Transition probabilities for symmetric jump processes”, Trans. Amer. Math. Soc., 354 (2002), 2933–2953
[4] R. F. Bass, T. Kumagai, “Symmetric Markov chains on $\mathbb{Z}^d$ with unbounded range”, Trans. Amer. Math. Soc., 360:4 (2008), 2041–2075
[5] R. F. Bass, T. Kumagai, T. Uemura, “Convergence of symmetric Markov chains on $Z^d$”, Probab. Theory Relat. Fields., 148 (2010), 107–140
[6] Theor. Probab. Math. Stat., 79 (2009), 23–38
[7] E. A. Carlen, S. Kusuoka, D. W. Stroock, “Upper bounds for symmetric Markov transition functions”, Ann. Inst. Poincaré, 2 (1987), 245–287
[8] Z.-Q. Chen, P. Kim, T. Kumagai, “Weighted Poincaré inequality and heat kernel estimates for finite range jump processes”, Math. Ann., 342(4) (2008), 833–883
[9] Z.-Q. Chen, P. Kim, T. Kumagai, “On Heat kernel estimates and parabolic Harnack inequality for jump processes on metric measure spaces”, Acta Math. Sin. (Engl. Ser.), 25 (2009), 1067–1086
[10] Z.-Q. Chen, P. Kim, T. Kumagai, “Global heat kernel estimates for symmetric jump processes”, Trans. Amer. Math. Soc., 363 (2011), 5021–5055
[11] Z.-Q. Chen, T. Kumagai, “Heat kernel estimates for stable-like processes on $d$-sets”, Stoch. Proc. Appl., 108, 27–62
[12] Z.-Q. Chen, T. Kumagai, “Heat kernel estimates for jump processes of mixed types on metric measure spaces”, Probab. Th. Rel. Fields., 140:1-2 (2008), 277–317
[13] E. T. Copson, Asymptotic expansions, Cambridge Uni. Press, Cambridge, 1965
[14] M. V. Fedoryuk, The saddle point method, Nauka, Moscow, 1977 (in Russian)
[15] I. I. Gikhman, A. V. Skorokhod, Stochastic differential equations and their applications, Naukova Dumka, Kiev, 1982 (in Russian)
[16] N. Jacob, V. Knopova, S. Landwehr, R. L. Schilling, A geometric interpretation of the transition density of a Lévy process (to appear)
[17] P. Hartman, A. Wintner, “On the infinitesimal generators of integral convolutions”, Am. J. Math., 64 (1942), 273–298
[18] V. P. Knopova, A. M. Kulik, “Exact asymptotic for distribution densities of Lévy functionals”, Electronic J. Prob., 16 (2011), 1394–1433
[19] V. P. Knopova, A. M. Kulik, Asymptotic behaviour of the distribution density of the fractional Lévy motion, 2011, arXiv: 1112.0497
[20] V. P. Knopova, R. S. Schilling, “Transition Density Estimates for a Class of Lévy and Lévy-Type Processes”, J. Theor. Prob. (to appear)
[21] V. P. Knopova, R. S. Schilling, “A note on the existence of transition probability densities of Lévy processes”, Forum Math. (to appear)
[22] A. M. Kulik, Absolute continuity and convergence in variation for distributions of a functionals of Poisson point measure, 2008, arXiv: 0803.2389
[23] A. M. Kulik, “Exponential ergodicity of the solutions to SDE's with a jump noise”, Stochastic Process. Appl., 119:2 (2009), 602–632
[24] A. M. Kulik, “Asymptotic and spectral properties of exponentially $\varphi$-ergodic Markov processes”, Stoch. Proc. Appl., 121 (2011), 1044–1075
[25] H. Masuda, “Ergodicity and exponential $\beta$-mixing bounds for multidimensional diffusions with jumps”, Stoch. Proc. Appl., 117 (2007), 35–56
[26] P. Lancaster, Theory of matrices, Academic Press, New York, 1969
[27] B. S. Rajput, J. Rosinski, “Spectral representations of infinitely divisible processes”, Prob. Th. Rel. Fields, 82 (1989), 451–487
[28] R. T. Rockafellar, R. J.-B. Wets, Variational Analysis, Springer, Berlin, 1997
[29] R. T. Rockafellar, Convex Analysis, Second ed., Princeton University Press, USA, 1972
[30] B. V. Shabat, Introduction to Complex Analysis, v. II, Functions of several variables, AMS, USA, 1992