10：PH分布基本理论

112™™™™™3™™™™™™™4™™()1,(),0xxFxefxexλλλ−−=−=≥01(),()(),Re0sxEXfsefxdxssλλλ∞−===≥+∫%5™9()1(){|}1()ststFstePXstXteFteλλλ−+−−−++===−™9“”6™()1,0,01xFxexλαα−=−≥≤≤™αα27™99™™(),()1EXfssααλαλλ==−++%0()(1)()(1),0xFxUxexλαα−=−+−≥8™9™999™99910™9™999™911–∑=−−=kjjtjjejttF1!)(1)(µµ12∑=−−=kjtjjetF1)1()(µα™™313™™™™™™™14™9⎟⎟⎠⎞⎜⎜⎝⎛=000TTQm}{1,2,L}1m,m,2,1{+L15™9ijT0iT),2,1,(mjiL=),2,1(miL=⎟⎟⎠⎞⎜⎜⎝⎛=000TTQ16™9900TeT+=00,0(),0iiijiTTijT≥≠≥},2,1{mL},2,1{mL17™99eTxxF)exp(1)(α−iα),,,(21mααααL=1=eα18419™99)1,,,2,1(])([)(+===mmjjxYPxvjLmj,,2,1L=jjvα=)0(1[()][()|()][()]miPYxxjPYxxjYxiPYxi=+∆==+∆===∑20™∑==miijijTxvxV1')()(TxVxV)()('=))(,),(),(()(21xvxvxvxVmL=xxvxvxTxxvTxxvxxvmjiijjjjiijjj∆−∆++∆=∆−∆+∑≠=,1)()()1()()()(21™π=)0(VTxVxV)()('=)exp()(TxxVα=∑=−=−==−=+==mjeTxexvjxYpmxYpxF1)exp(1)(1])([1]1)([)(α22™!)()exp(0nTxTxnn∑∞==nTnx23™9™9™924™™™™0)exp()(TTxxfα=01*)()(TTsIsf−−=αeTkTTkkkkkk−+−−=−=ααµ!)1(!)1(0)1(xxexFλ−∞→−=1)(lim525™9™926™99⎟⎟⎠⎞⎜⎜⎝⎛=100TTP}1,,,2,1{+mmL},,2,1{mL1+mijT),2,1,(mjiL=0iT),2,1(miL=27™9)1(,0110≥==−+kTTppkkmααiα28™™™™29K30∑=−−=KjtjjjejttF1!)(1)(µµ⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎣⎡=⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎣⎡−−−−==−−kkkkkTTµµµµµµµµα00000)0,0,0,1(0112211MOO43421L631),,,(21kααααL=32∑=−−=kjtjjetF1)1()(µα⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡=⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡−−−=kkTTµµµµµµMO21021003334™9™9∞ba0)1,0(∈σ⎭⎬⎫==−==σσ}{1}{bSpaSP35™NabaS)(−+=σσ−====1}0{,}1{NPNPlkkEEE*)1(σσ+−™36™™kElE∞→k)/(abl−∞→llk+jσjσ−11≥k737™™1,,2,1−=kjL∏−=++−[phone])]exp(**)[exp()exp(*)exp()1()exp(kjkjµµσµµσσµσLL)1,0(∈jσ0=kσ38™™™™™™™39™—™™eTxxF)exp(1)(α−=eSyxG)exp(1)(β−=),(Lγ[]⎟⎟⎠⎞⎜⎜⎝⎛==STTL00,0βαγ40™),(Lγ[]010101101101)()(0)(0)()()(0,)(SSsITTsISSsISsITTsITsILLsI−−−−−−−−−=⎥⎦⎤⎢⎣⎡⎥⎦⎤⎢⎣⎡−−−−−=−βαβαγ41™99()01=α⎟⎟⎠⎞⎜⎜⎝⎛−−=2110λλλT),(Tα),(Sβ1=β3λ−=S42™()()0010==αγ⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡−−−=322110000λλλλλL843™9),(Tα),(Tπ0)(0=+απTT1=eπ44™eTxTdyeTydyyFxF]1)[exp()exp()](1[)(100*−==−=−∫∫µααµµππ0)(0=+απTT1=eπ1010)(−−−=−=TTTTαπαππ45™™™™PHeTTe10)(1−−==αππµπ=0Tπµα11−=−TeTxeTxxF)exp(1]1)[exp()(*ππ−=−−=)(*xF),(Tπ46™9∑=kjjixFq1)(jX))(),((jTjα)(xFj),(Tα)](,),1([1kqqkαααL=()()⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛=kTTT001O47™iiiTλα−==,1),,(1kppL=α⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡−−=kTλλO1),,{1kXXLkH48™99),(Tα)(xF),(Sβ)(yG),(Lγ),(Γ∆nmmn++949[]00βα⊗=∆⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡⊗⊗⊗+⊗=ΓSTITSISIIT000000)(βαγ⊗=SIITL⊗+⊗=50™9),(SXβ−),(TXα−51),min(^^YXZ=SIIT⊗+⊗ST⊕52™9⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡≡⊗BaBaBaBaBaBaBaBaBaBAmnmmnnLMMMMLL212222111211nm×BA⊗nmRA×∈qpRB×∈qp×53™9BIIABAmn⊗+⊗=⊕mm×mmRA×∈nn×nnRB×∈BA⊕mInI54™™CBCACBA⊗+⊗=⊗+)(BCACBAC⊗+⊗=+⊗)(CBACBA⊗⊗=⊗⊗)()()())((CDABDBCA⊗=⊗⊗1055™™DBCBDACADCBA⊗+⊗+⊗+⊗=+⊗+)()(TTTBABA⊗=⊗)(KKKBABA⊗=⊗)(111)(−−−⊗=⊗BABA56™kkkBAAB⋅≠)(AAAAk⊗⊗⊗=L][][][][)(kkkBAAB⋅=™Kronecker’sPower™Kronecker57™)()()(BABAlkiλλλ⋅=⊗),,1;,,1;,,1(nminlmk×===LLL)()()(BABAlkiλλλ+=⊕),,1;,,1;,,1(nminlmk×===LLL)(AiλnnCB×∈mmCA×∈™58™9000STL⊗=βαγ⊗=11++=nmnβγSTITL⊗⋅+⊗=α0mn)(•F}{vSnS),(βmT),(α∑∞=•0)()(vvvFS59™etsstW⋅+−=])exp[(1)(0θρρϖ60™99ρθγ=00θρSSL+=),(Sβθβ0SS+1161™.),(Sθ)(^•Fkρρ)1(−),(ρρ),(ρρ),(SθkkkssfsfsW∑∞=−⎟⎟⎠⎞⎜⎜⎝⎛⋅−−=−−=01^)(1)1()(11)(µρρρρ62™9w⊗=ρθγxKSKSISL000⊗+⊗+⊗=βρβ/PH/1M[PH]),(Kk}{ig),(Sβ)(xF63™PH`M/PH`/1/PH/1M[PH]∑∞==1)(1)()(ivixFgxF64™49PH9(*)(**)KSIST0⊗β+⊗=k⊗=βαXKK⊗+0β⊗+0SS)(1xFαθw65™9)(•F),(Tα∫∞−=0)(!)(µλµαλµdFkekk1)(−−=TIλλαγ1)(−−=TiLλλ011)(TTIm−+−=λαγ010)(TTiL−−=λ66[]{}[]{}[][][]0111101011110111011010)()()()()()()()()()()()()()()(TTITIzITIzTTITTITIzITIzTIzITTIzTIITzTIITITTIzzfzazAkkk−−−−−−−−−−−−−−−+∞=−−−⋅−+−=−−−−+−−=−−−=−−−=−−=−==∑λλλλαλλαλλλλλλλαλλλαλλλαλλαλλ1267™1)()()()()()())(()()()()1(101101011101=−−=+−=−+−=−−−−+−=−−−−−−−−eTITIIeTTIeTITTITTITITTITTIAλλαλλαλλαλαλλλλαλα68™969™™™™™™’7071™™1=αλ−=Tλ=0Tλ()21,,rrλ()0,1=α⎟⎟⎠⎞⎜⎜⎝⎛−−−=2211rrrrTλ⎟⎟⎠⎞⎜⎜⎝⎛=00λT721373™99()T,αα0TTQ+=)(tN(],0t)(tJ{}),(),(tnPtnPij=74™TtPtTPtP),0(),0(),0`(==])0(,0)0(|)(,)([),(iJNjtJntNPtnPij=====αα00),1(),(),1(),(),`(TtnPTtnPtnPTtnTPtnP−+=−+=),(tnP75∑∞==0*),(),(nnztnPtzP),()(),(),(),1(),(),(*0*00010*tzPZTTtzPTztnPTztnPTztnTPtzPznnnnnnααα+=+=−+=∂∂∑∑∑∞=∞=∞=])exp[(),(0*tzTTtzPα+=76™∫∫∑∑∑∫∑∑∑∑==⎥⎦⎤⎢⎣⎡=⎥⎦⎤⎢⎣⎡+−⎥⎦⎤⎢⎣⎡=∂∂∞=∞==−∞=−=−+−∞=−=−−=ttnnnnnvvnvtnnnvvnvnnnvvnvnzduTuQeQTQnueQTQdunueQTQnteQTQntetzpz00*00*00*00*0*0010*0*111101*0*1*)exp(!!)!11(!|),(αααα77™9eTtQtduTuQuQduTuQetnnPtHtnt1*222002**100*)]exp([2]!2)([)exp(),()(−−−∞=−+++=+++===∑∑∫πµαµµσµαααααLα78™9ttTduTuQuQduTuQtFtµππππαπ==+++==∫∫002**00*]!2)([)exp()(Lπ147980™9]|,[],,;,,|,[110011nnnnnnnJjJtXPXXJJjJtXP=≤==≤++++L(){}nnJX,1+nXnJ(){}nnJX,81™0)exp()(TTttfα=™),(Tα8283rI=α⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡−−−−−−=111121112222211112111rrrrrrrrrrrrrrrrTλλλLMMMMLL),,,(1210rdiagTλλλL=84’™()TkkkT0,,α()TT0111,,α()TT0222,,α21rr×1585’⎥⎦⎤⎢⎣⎡⊗⊗=2121αααrrsII2121TIITTrrs⊗+⊗=[]TTTrrsII0212010⊗⊗=86™87