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Publié par | profil-zyak-2012 |
Nombre de lectures | 18 |
Langue | English |
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GaussianapproximationswithmoreerederedMalliaFvinofcalculusSciencesIvsuppanacceptingNourdinremarkUnivfeaturesersit?hdebLorraine,aInstituttodeyMath?matiquesbut?lielongCartantralB.Pey.originates70239,b54506annVbandoineuvre-l?s-NancyACedex,SciencesFandrancetinourdin@gmail.comparticipanMarcGiohthe20th,nice2012conOvlectureserviewin.limitInTheatroseminaltpapoferColl?geofJan2005,framewNualarttheandaris.Paeccatiin[37]nddiscoshortvtseredtheaarissurprisingacademiccenthetraloutlimitthetheoremgrateful(calledlecturesthethankFeccati,ourthaMomenedtecially!)Theoremreceninhoponwythesequel)thefor.sequencesnewofolvingmnon-cenultipleforstoGaussiancthastictointhetegralsthisof.aaxedIorder:atinFthiswconandtext,withinconofvprizeergenceondationindedistributionmatoseentheforstandardoknormalhlareaderwucisinequiveyalenknotIttotoconondationvdeergenceitsofduringjustearthegivingfourthortunitmomeneakt.yShortlyhafterwColl?geards,IPalleccatiofandtheirTMyudores[44]annigaonlyvgive(resultingadevmSectionultidimensional(andvallersionwofdiscothisIcitharacterization.ueSinceytheppublicationouofatctheseofthttp://www.sciencesmaths-wsomeoablebresultseautifulvpapceners,andmantralytheoremsimprofunctionalsvinnite-dimensionalemenelds.tscurrenandsurvdevaimselopmenintsduceonmainthisofthemerecenhatheoryvItefrombserieseenlecturesconsidered.delivLecturesAmongthemtheisdetherancewetorkeenbuaryyMarcNualart2012,andtheOrtiz-Latorreork[36],thegivingualaofnewFprodesofMath?matiquesonlyPbasedItonyMalliaevinascalculusteaserandthetheouse[29],ofwhicinthetegrationterestedbwillympartshonthanWienerthisspace.survA.secondcstepwledgmenis.misypleasurejointhanktFpapdeserMath?matiques[25]P(writtenforingenerouscollabortorationthewithyP2011-12eccati)forinmewhicopph,ybspyabbringingmtogetherrecenStein'sresearcmethoindprestigiouswithdeMalliarance.vinamcalculus,towtheetshathesevforeassiduitb.eenlastablego(amongtoothervthings)Ptonotassoforciatetoquanetitativlectureetobmaterialoundseloptointhe10)FalsoourthespMomenforttheTheorem.theoremsIteturnstlyoutvthattogether.Stein'sdomethoedwillandtinMalliathisvinacalculusastastogetherossible!admirablyYwmaell.wTheirhinvideosteractionthehasatledparis.fr/index.php?page=175to1{X }k k>1
ρ :Z→R E[X X ] =ρ(k−l) k,l> 1 ρ(0) = 1k l
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q=d k=1 p,q=d k,l=1
∞ n ∞∑ ∑ ∑ ∑ ( )1 |r|2 q 2 q= q!a ρ(k−l) = q!a ρ(r) 1− 1 .{|r|<n}q qn n
q=d k,l=1 q=d r∈Z
q>d r∈Z
( )|r|2 q 2 qq!a ρ(r) 1− 1 →q!a ρ(r) n→∞.{|r|<n}q qn
√
2 2|ρ(k)| =|E[X X ]|6 E[X ]E[X ] = 11 k+1 1 1+k
( )|r|2 q 2 q 2 dq!a |ρ(r)| 1− 1 6q!a |ρ(r)| 6q!a |ρ(r)| ,{|r|<n}q q qn
∑ ∑ ∑∞ 2 d 2 dq!a |ρ(r)| =E[φ (X )]× |ρ(r)| <∞1q=d r∈Z q r∈Z
2 2 2E[V ]→σ n→∞ σ ∈ [0,∞)n
φ =H q> 1q
φ =P ∈R[X]
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22 −x /2φ φ ∈ L (R,e dx)
N> 1
N n ∞ n∑ ∑ ∑ ∑1 1
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q=d k=1 q=N+1 k=1
∞∑ ∑
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n>1
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N n→∞
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q=d k∈Z
law 2V =V +R → N(0,σ ) n→∞n n,N n,N
{X }k k>1
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H := span{X ,X ,...}1 2
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∫
∞
ρ(k−l) =E[X X ] = e (x)e (x)dx, k,l> 1k l k l
0
B = (B )t t>0
{∫ }∞