Fisher information estimates for Boltzmann's collision operator
Tài liệu tham khảo
Barron, 1986, Entropy and the central limit theorem, Ann. Probab., 14, 336, 10.1214/aop/1176992632
Blachman, 1965, The convolution inequality for entropy powers, IEEE Trans. Info., 2, 267, 10.1109/TIT.1965.1053768
Bobylev, 1988, The theory of the nonlinear, spatially uniform Boltzmann equation for Maxwellian molecules, Sov. Sci. Rev. C. Math. Phys., 7, 111
Bobylev, 1992, On the generalization of the Boltzmann H-theorem for a spatially homogeneous Maxwell gas, J. Math. Phys., 33, 2578, 10.1063/1.529578
Carlen, 1991, Superadditivity of Fisher's information and logarithmic Sobolev inequalities, J. Funct. Anal., 101, 194, 10.1016/0022-1236(91)90155-X
E. A. Carlen, Personal communication.
Carlen, 1992, Strict entropy production bounds and stability of the rate of convergence to equilibrium for the Boltzmann equation, J. Stat. Phys., 67, 575, 10.1007/BF01049721
Carlen, 1994, Entropy production estimates for Boltzmann equations with physically realistic collision kernels, J. Stat. Phys., 74, 743, 10.1007/BF02188578
E. A. Carlen, E. Gabetta and G. Toscani, Propagation of smoothness in velocities and strong exponential convergence for Maxwellian molecules, Georgia Tech. and Pavia Preprint. To appear in Comm. Math. Phys.
Carlen, 1991, Entropy production by block variable summation and central limit theorems, Comm. Math. Phys., 140, 339, 10.1007/BF02099503
Fisher, 1925, Theory of statistical estimation, 22, 700
Linnik, 1959, An information-theoretic proof of the central limit theorem with the Lindenberg condition, Th. Prob. Appl., 4, 288, 10.1137/1104028
Lions, 1994, Compactness in Boltzmann's equation via Fourier integral operators and applications, J. Math. Kyoto Univ., 34, 391, 10.1215/kjm/1250519017
McKean, 1966, Speed of approach to equilibrium for Kac's caricature of a Maxwellian gas, Arch. Rat. Mech. Anal., 21, 343, 10.1007/BF00264463
S. Mischler, Personal communication.
Stam, 1959, Some inequalities satisfied by the quantities of information of Fisher and Shannon, Inform. Control, 2, 101, 10.1016/S0019-9958(59)90348-1
Toscani, 1997
Toscani, 1992, New a priori estimates for the spatially homogeneous Boltzmann equation, Cont. Mech. Thermodyn., 4, 81, 10.1007/BF01125691
Toscani, 1995, Strong Convergence in LP for a spatially homogeneous Maxwell gas with cut-off, Transp. Theory Stat. Phys., 24, 319, 10.1080/00411459508205132
Toscani, 1997
