LEADER 03444nam 22006732 450 001 9910457725103321 005 20151005020622.0 010 $a1-107-15008-6 010 $a1-280-47800-4 010 $a9786610478002 010 $a0-511-19542-7 010 $a0-511-19608-3 010 $a0-511-19404-8 010 $a0-511-31440-X 010 $a0-511-54662-9 010 $a0-511-19478-1 035 $a(CKB)1000000000353018 035 $a(EBL)259909 035 $a(OCoLC)171138818 035 $a(SSID)ssj0000191673 035 $a(PQKBManifestationID)11166022 035 $a(PQKBTitleCode)TC0000191673 035 $a(PQKBWorkID)10184408 035 $a(PQKB)11514941 035 $a(UkCbUP)CR9780511546624 035 $a(OCoLC)144618355 035 $a(MiAaPQ)EBC259909 035 $a(Au-PeEL)EBL259909 035 $a(CaPaEBR)ebr10130356 035 $a(CaONFJC)MIL47800 035 $a(EXLCZ)991000000000353018 100 $a20090508d2004|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLe?vy processes in Lie groups /$fMing Liao$b[electronic resource] 210 1$aCambridge :$cCambridge University Press,$d2004. 215 $a1 online resource (x, 266 pages) $cdigital, PDF file(s) 225 1 $aCambridge tracts in mathematics ;$v162 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 $a0-521-83653-0 320 $aIncludes bibliographical references and index. 327 $aCover; Half-title; Title; Copyright; Contents; Preface; List of Symbols; Introduction; 1 Le?vy Processes in Lie Groups; 2 Induced Processes; 3 Generator and Stochastic Integral Equation of a Le?vy Process; 4 Le?vy Processes in Compact Lie Groups and Fourier Analysis; 5 Semi-simple Lie Groups of Noncompact Type; 6 Limiting Properties of Le?vy Processes; 7 Rate of Convergence; 8 Le?vy Processes as Stochastic Flows; Appendix A Lie Groups; Appendix B Stochastic Analysis; Bibliography; Index 330 $aThe theory of Le?vy processes in Lie groups is not merely an extension of the theory of Le?vy processes in Euclidean spaces. Because of the unique structures possessed by non-commutative Lie groups, these processes exhibit certain interesting limiting properties which are not present for their counterparts in Euclidean spaces. These properties reveal a deep connection between the behaviour of the stochastic processes and the underlying algebraic and geometric structures of the Lie groups themselves. The purpose of this work is to provide an introduction to Le?vy processes in general Lie groups, the limiting properties of Le?vy processes in semi-simple Lie groups of non-compact type and the dynamical behavior of such processes as stochastic flows on certain homogeneous spaces. The reader is assumed to be familiar with Lie groups and stochastic analysis, but no prior knowledge of semi-simple Lie groups is required. 410 0$aCambridge tracts in mathematics ;$v162. 606 $aLe?vy processes 606 $aLie groups 615 0$aLe?vy processes. 615 0$aLie groups. 676 $a512/.482 700 $aLiao$b Ming$c(Mathematician),$01032934 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910457725103321 996 $aLe?vy processes in Lie groups$92451115 997 $aUNINA