溷沌时间序列和分形统计理论及应用

上海交通大学硕士学位论文混沌时间序列和分形统计理论及应用姓名：张可申请学位级别：硕士专业：系统理论指导教师：宋宝瑞2004011212120041122456XdXXw→:Xwwxwwxxw=)(Xx∈},2,1,0:)({0L=nxwnwxNnwXn,,2,1,;L=ssHHW→:7)()()()(21BwBwBwBWNULUU=HB∈∀HCB∈,),())(),((CBshBWBWh≤WHA∈)()(1AwAWAnNn===UHB∈)(lim0BWAnn∞→=ANnwXn,,2,1,;L=)()()(**EEEmmm==e⊂⊂me)1ln(),(ln0eeeANiml→112221XX→=q11)(1Aq1)(1Aq8VfVVdVx∈xeynd))(),((yfxfdnnVXYkYXfk∩)(fV91102113mmmmmnNr1N1ryN1N12y))(),((),(1yxyxyyrr=),(Nyx∈∀Nr1N1r1N1r2N2r0N2r1N1r2N2rMdyMMyyMR12:),(+→ΦdRMyy))]((,)),(()),((),([),(122xyxyxyxyyd+=ΦyyyyL),(yyΦM12+dRNxxx,,,21LLmt)])1((,),2(),(),([)(ttt-+++=mtxtxtxtxtYiiiiiLLLL,2,1=i134Nxxx,,,21LLjjNxx=+jiNiijxxNC+=∑=11NkjijkeCpp2∑=kpkpkix14nllll≥≥≥≥L321∑il1l1l1l∑-=∞→-=+++10'021)()(ln1limniikiknnktAtAttlllL∑=--=MkkkmtLtLtt11201)()(log1l)(ktLkt0t)(0tL1t)(1tL1l01l01l154.2.L321,,xxx12+≥DnDn),,,,()1(2ttt-+++=njjjjjxxxxyLjyjkiknkjiyyyy-=-≤≤1maxrN2N∑=--=NjijinyyrNrC1,2)(1)(qq0,00,1{)(=xxxq)(rCn0→rr)(lim0rCnr→Dr16DrDrrCDnGPln)(ln=rrnD)(lnrCnrln∞DLLLL,,,,,121nnxxxx-tm0m)])1((,),2(),(),([)(ttt-+++=mtxtxtxtxtYiiiiiLLLL,2,1=i∑=∞→--=NjijiNtYtYrNrC1,))()((1)(limq0,00,1{)(=xxxqrd)(rCrrCmdln/)(ln)(=0m)(0md1m0m)(mdmd17)(itYtttt]20[t+txttmLyapunovmD1852R),(iiyxiNNxxxL10)(xf)(xf0xNxRiiyxf=)(iN2RiwiN)(xf2RiwiNiwiw2R2R⎟⎟⎠⎞⎜⎜⎝⎛yxiw⎟⎟⎠⎞⎜⎜⎝⎛yx⎟⎟⎠⎞⎜⎜⎝⎛iiidca0⎟⎟⎠⎞⎜⎜⎝⎛yx⎟⎟⎠⎞⎜⎜⎝⎛iifeiNiw⎟⎟⎠⎞⎜⎜⎝⎛00yx⎟⎟⎠⎞⎜⎜⎝⎛--11iiyxiw⎟⎟⎠⎞⎜⎜⎝⎛NNyx⎟⎟⎠⎞⎜⎜⎝⎛iiyxiiwiaicidieif⎪⎪⎩⎪⎪⎨⎧=++=++=+=+--iiNiNiiiiiiiNiiiiyfydxcyfydxcxexaxexa10010iwidididiw19⎪⎪⎪⎪⎩⎪⎪⎪⎪⎨⎧-----=--=-----=--=----000001001000101xxxyyxdxxyxyxfxxxxxxexxyydxxyycxxxxaNNNiNiiNiNiiNiNNiNiiiNiii)),(),((),(yxFxLyxiii=wiaicieif0101))(()(xxxxxxxxLNiiii---+=--100010)()())()((),(--+-+-----=iiNNiiiiyyydxxyydyyxxyxF2RiwiN2RiwiNGRxxfn→],[0ixiyiN]),([0nxxfG=ididixiyiN2RiwiN∑=-=Nidiiad111ixiyNxxxxaNiii101=--=-20NdDNiilog]log[11∑=+=idN),(jiZHjj2/1-=dd),()1,(),(jijjijiRZZd+=-jijd),(jiR∈),(jiRixiyiNDid934.02loglog--==NNdDiiN216}),({TttX∈10,0,),()(∀∈=-HaTtatXatXHfd)(tXtHH227LL,,21ttLL,,21dd1t2t1t2t1t≤2t1t≥2tee-∈dtDbat)(sup],[≤≤23248)(aaf-)(limaannxx∞→=axmxameamaeaaxr),(lim),(0aaddaammxHxHrr→=)(af⎪⎩⎪⎨⎧=∞=)()()(0),(aaamaafrfrfrxHr)(af)(afax)(aNrrNxHeamaae)().(=)(aN)(aef-).(aaemxHreaaeln/)(lnlim)(0Nf→-=)(aaf-a25aaaaa)(af)(qDq-xiΔmi∫Δ=ixdpi)(mr∑=⋅==1)()()(irrqirqNpqMeeeee)(lim)(0qMqMrree→=ipq)(qt⎪⎩⎪⎨⎧=∞=)()()(0)(qrqrqrqMrttt)(qtqD⎪⎩⎪⎨⎧=≠⋅-=∑=→→1ln/)(ln)(lim1ln/)(lnlim11100qppqqNqDiiiqeeeeeee)(qDq-)]()][1/(1[aafqqDq--=)()(qqftaa-=26qDqq)1()(-=tdqDqddqqdqq)1(/)()(-==ta))((dmixTq∑==ddmdNiqTxiqS1)())(()(∞∞-qq)(qSd)(qtd-)(qt)(qtq)(qa))((qaf)())(()(qqaqafq-=t)()(qaqdqd-=tqtafq)(qt)(qa))((qaf)(jqSidiMjNNNi=m27NiNiLLi=miLnXnNkdi∑==++-=112121)1)((mjjjiXXLiiXmmXL∑∑==iiiLL1mnN∑=-+-=ijjjXXiLL12121)1)(()(iN)(NLLL=kq102/-=kkdd0dLLi=mkdim))1(()(kkiiLLiLLLdd⋅--⋅=i)/(kNd),(kqNd1≤kd1+=kk),(lnkqNdkdlnqD28qd)(tP)(tX)(lntP)0(lnPNtΔ∑-=ΔΔ=Δ10),(),(NiqqttiXtTSTqctqtTSEqln)()ln()()],([ln+Δ=Δt))(()(tSEtSqqΔ≈Δ)ln(~)(lnttSqΔΔ)(qt)ln(~)]([lnttSEqΔΔqq0)]1([ln=qSE29)ln(tΔqq)]([lntSEqΔ)ln(tΔ)(qt)(qtq)(qtq)(qtqdqqda/)(t=)()(qaqaft-=)(af3031932),,,(21nxxxfYL=331eq+=),(xfyxye2s2s'21),,,(pqqqqL=pRfqfq)(DF34D/2D-D-1)2/(D-)25(D--)(DFqD+-DD-35aa-1-aaaaaaa1-aa2a1-a2-aaa-a362ParetoaxCN/=00≥xx0xC0aaxCN/=xaCNlglglg-=∑∑∑∑∑-⋅-=22)lg(lglglglglgxxnNxnNxanxaNC∑∑+=lglglg0xx3733ZAADDD∞→D0→t384SARSD0rD390r0r0r0r400r0r414243444546