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8¢%¸G¥¾8F¤.»t¢? i¢¡?XÅd<d `¾8FtÜ<*/X¾¹ÂFY·
`?¤<i FF¤XYX¢Y¤qw*?d `Y<³`we<¾?X Fit`ºA 8
F¢?¤.bÒ F? Fd¡n² FY.XF i
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פ.n¼X%i F?8·ºA8tX´ÄFI.XFY*¢itX
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F*<dF¡{*`8¢
587.6
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55.1
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XF¢? Fd¡?´¹dn¤»nY¢YXF¤{*`8d?¤{?d `?8³`nn¤F
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F?·n 1 E[T ] σ[T ]
]
7nêPãYêê â?â`ä7
â ê;o;Iâné ã1;p8IéI;
ã ;o;tâFäê ç?ênê;Iä
ç â`êPé?ãtã ãR8Pçnät7
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¬YØ Ù
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n 1
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99 %
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α r = r −1 X r j=1
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8n<8
n
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0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
0 500 1000 1500 2000 2500
τ
epocas
E[T−τ|T>τ]
E[T]
"ab_`mPQ[O | %
E[T − τ |T > τ ]
jXZ`UVZ&f¥mPWPjXaby`W¹\PMτ
<¤X?8:i¢¾À? iXd `%F¤
r = 10 1 n
4¨n¤eXF¤.8bY·8?¤e8X??X Fdn<?£<<Äi¤AX¢ÄY Fd¡n
ˆ
α r = 1.942
¬Fn8¤.d¤AXFIXq F?¾t<i¤A.
Ã
d¡?XF¤.d¤e±I<{¢' i?·
¢%iXF Ã *
T
XdF< 8F F?d*dFIX*ndd<¡n*d F¸¹XF8<Y$YtXV¢Y¤ F?8d Fd?<F¤$¥¡n8`?¤$Y
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s t ?ÉYÊJEÉn5K+ÎuEeÍE$Ì ËvGuE¾Ì ÎS?ÉYÊIÎB! ÍÎSÏ4
:Í8Ë+ ËÍ8ÎSÌE
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E[S]
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<¤XYV¥F¤A.YXi§n¢*XF Fn*dF8³Fn¤
S = (t 1 , t 2 , t 3 , . . .)
¬Fn
t i ∈ Z + ∪{∞}
nÞeiÒ<<d*n¤p
in*e¢e¢¤A.Xb·¼<8 Fd¡n ¢q»?YX¢?¼8d?d`wX?X¢
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t
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Fd¡n´ d¤A.X¢¼8< Fd¡?
p(t)
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×
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S t = (t, t, . . .)
¬8¸l p
F+»??dYqiÒ8¢8¹ in*
l p ≡ inf
t<∞ E[S t ]
|n}F~1~pp 1~p ??-~p?-b
E[S] ≡ E[T S ]
b? b1 &1 b-J?-p &
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S t ∗ = (t ∗ , t ∗ , . . .)
F¤!¢F¤A.YXF§?¢¡n8XdÄ'Y
p
¬¤.¢i8t ∗<:»??dYq±I8e F<*8d
t ∗ =
( t
?+±I<E[S t ] = l p
∞
¤.@ l p .
¤AX%XF¤.<bn£XF8< i:FXn¼<dFÄ´:F8 Fn·
.Y¢ i¤A.YXF§?¥ ¡n8XdÄ F?d F<¢w{F»nY¢Y{8
t
±I<e*d8¢*d³`'¢¹F F<? Fd¡nE[S t ] = 1
q(t) t − X
t 0 <t
q(t 0 )
!
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t 0 ≤t p(t 0 )i¤e¢ÄÆg<< i¢¡?£8 8d¤A·
.X¢¼8< Fd¡?¯Y F< <¢n8
p
¤?¤.d¼<dGF8 Fn·.YX¤.: in¯Æg<8 Fdn<i¤*8:8d¤A.Xd¼<< i¢¡?©<Y´¥Y¤
FY¢i¤<'i袤A'<Ä*Åd<d*VÒ8dX ×n§8áéYåÚëtF
F¤.: `Y¤.8¬¸°?{ F?*d<8d `´F¿4F?XiĽãI¬¥
F¤A.YXF§?¢'XF Fn*dF8³Fn¤¤.iÀ
(∞, ∞, . . .)
¬P^n<¹8¤XY<d8§n<<¹F¤A.wXF§n¢*8&XF Fn*dF8³Fn¤F
ѧnF8i?^¬{ièd¤AXFÑ8?¤Gd¢*bY Fdn<i¤G8ÀY i·
X¢ F?¤´wÝF¤A©nXd*¢³F? Fd¡nVÓ8Xd*i´d·
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¼<< i¢¡?
q(t)
8FXdF*¾8'Ò<?dd³`? Fd¡?8FF·.XFY*¢itX¬??<<±I<!¤.dF*X¤.<<F8!F¤AXdÄw
.`»PÂF¤8 ¤. Æ8< Fd¡?*8d¤A.X¢¼8< Fd¡?F*<ÅbXd `
ˆ
q(t)
%¤.F§?<¹d<§nY`¬¤.<i¢qi袤AXb{8¾tÜ<*/·X8&ÂFI `Y¤*Åd8¢*
t min
?F¼`ºA*F FY
ˆ
p(t) = 0
¬¸¾<G»??dYqÄÀwè8d*t max
8F¤AÆg<iX³F
Fn*88? i¢?Y F°i! FY ¤.¾8iXdF8*¢´[ºAF F·
Fd¡nY<<±t8 8q¤.
Ã
F¸t?d `Y<³`?8
δ
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q(t max ) = 1
×i£t8F¤A.X¾[ºAF*8¢t min = 85
¸t max = 10000
Ú Ø Y*Fdd8¬F!Xn¼8¢iÄ´À? iXb·F¹ F?<¤.d¤AXVF¾¹<i¤A.X`YdÄÀwè¢*?¤.¢¼8dV¥
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T
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1 ˆ
q(t) t − X
t 0 <t
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!
Fn
t ∈ {t min , t min + 1, . . . , t max − 1, t max }
¨+Äô¢§?8*ç*¹8F¤A.¹FXdF**F¤.i?8Ä8
FI.XFY*¢itX¾wG»nwX¢?¤ »??dYXF¤
t
¬4^n<Y»nwX¥Y¤:F¤A.wXF§n¢Y¤
S t
{¨+?¤¾XdF*?¤¾F¤./n8?¤
¤.n:i¤AX¢ÄY Fdn8F¤ `?d F8¢n<Y¤&8¤X?<8'¥'Æ<8 Fd¡n
8*¢¤A.Xd¼8< Fd¡ni*<ÅbXd `
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q(t)
?¼8XF8¥8G:<Y.·Xd£½¢?¤
1000
¹8F¤A.?¤«½XdF*n¤G8°F·.XFY*¢itX´F8X?¼<dFÄ´8i¤. iXbXF¶¢£¤.i i·
Fd¡n ?IXiXd?`3q¼8¤.iX»??*n¤±I<
t ∗ = 418
¸0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
600 800 1000 1200 1400 1600 1800 2000
t
epocas
E[S t ] E[T]
"ab_`mPQTOo%RabMXUVNZMXl[NMXQ[OF\PZq\nM$MXWwRTQSMXWIOFUVabMXWYR[ZqNIOFQ[O
v`OFQSabZ`l4v`OFobZ`QSMXl
t
\PMQ[MXjXZ`UVabMXW)XZ{mPlAOFWP\nZodO!MXlSRTQ[OiRTMX_`adOS t
l p = 546.876
¬¤.dF<8 FX¢i* *`d ¤.dÄXF F?·*dF<³F?¤
E[T ] = 888.850
+48¤.Ä8V¢F¤A.YX/·§n¢
S t ∗
?8*FIe¥'iÒ i¢i< F¢'8FFI.XF<?*dF·
XFÄ<8 ]
¬t¤.dF*XiÄXÂ/X*¢8n¤$F¤.inn¤F
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q(t ∗ )
P«áéYå<¤.q88F¤A.YXi§n¢
S e t = (t 1 , t 2 , t 3 , . . .)
int i
8'¥Æg?.·
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— 1 q(t)
< i ≤ (k + 1)
— 1 q(t)
,
Fn8¤.d§n<dF<8Ñ< XF<8d*dFIX¤.¡nd¦8ÓÆ^? /X?
Fn8¤A?IXV?{i< FdĹe¢¹F¤A.wXF§n¢*¡nX¢Ät¬
E[ e S t ∗ ] = O(E[S t ∗ ]).
×8 Ú£¢Gôd§n8:¤.¹?8¢d `¾F¤A¾F¤A.wXF§n¢G%»nw·
Xdn¤»??d?Xi¤*8
q(t)
¬i< F?t.ÀYn¤.%F¡nX¢*F
q(t) = 0.5740
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4XdF*i¤.in±I<:¤.: Fn8¤.¢§?<«F¤
656.970
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26 %
8{*TºAYV¤.n¼8XE[T ]
I¿?¸ Fn*&8d F ¥& i? i¢¡?
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Ú e¢*8e¢¹¡?8XdÄ t ?ÉYÊJEÉn5K+ÎuEeÍE$Ì ËvGuE¾Ì ÎS?ÉYÊIÎB! ÍÎSÏ4
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0
500 1000 1500 2000 2500 3000 3500 4000 4500 5000
q(t)
epocas
E[S t ] E[T]
E[S t
*]
"ab_`mnQTO %abMXUVNtZ MXlTNtMXQ[OF\PZ\PMeMXWwRTQSMXWIOFUVabMXWYR[ZNIO
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q(t)
mPlTOFWP\PZ{odOMlSRTQ[OiR[M_`adOS e t
YpOFQ[O
j/OF\PO
q(t)
lTMMXl[R[abUVyE[ e S t ∗ ]
UVMX\PadOFWwR[M100
l[abUqmPodOjabZ`WnMl \PMR[abNtZ'zZ`WYR[MXj/OFQSobZ'\PM&odOevFOFQ[adOFPobM&OFobMOiRTZ`QSadO
S e t
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¨<¼I¸«iV?^4XF¤.FI?´F¤A%F¤A.YXi§n¢:F²áéYå
¸ÓFt<8 F¢? dn¤¤.¢§?<dFIXF¤n¤½Xi?XFÄY¤°±I<
ºA<IX?¤:F¹8F¤A.?¯¤.n8XdÄY¢¢8n?¤.dIX¡?Xd `
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s?]®z*ux
ÿ
e
S t (muestra, q(t)) i ← 1
t i ← 2 epocas ←
~ú÷
T ←
zIkxÿ
[
(muestra)
û
T ≤ t i
epocas ← epocas + T
¡
ö/ù1¢£
ùPýú½û
epocas ← epocas + t i
i ← i + 1
û
i
ü%÷úb1/q(t)c = 0
t i ← 2t i
ùPýú½û
ûdù
T > t i
öiùYþ! ö`ý
epocas
ùPýú
"ab_`mPQTO¤o%p+QSZ?jXMX\PabUVabMXWYR[Z*NIOFQ[OlTabU&mPodOFQodO v`OFQSadOFPobM
OFobMOiRTZ`QSadO
S e t
NOP5QRO:SyT{¥[W
Ø
w¹Xt<Y¤¢Y¤q¢¤A.Xd¼8< Fdn8F¤
p
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!!] ≤ 192E[S t ∗ ](log 2 E[S t ∗ ] + 5).
×; ÚNOP5QRO:SyTy¦DW
Ø
w FY¢±t8diF¤A.YXF§?¢
S
¬sup
p:l p =l
E[S] ≥ 1
8 E[S t ∗ ] log 2 (E[S t ∗ ]).
Ø
Y¾YIX8¬$F¤¾?¤.d¼<d´F< F?I.Y%<
p
YFY¢±t8diÄF¤A.YXi§n¢°±I< Ã ?§n°±I<%¤.¯XdF*
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XF§n¢
S
!! t XÂiX*d<n¤F¤.i?8?¤F¬S
!! F¤$¢*TºAY±I<!¤.8<` F?<¤.F§?<b ¤.d Fn8I Fd*¢itX
¹8XdYX+¤.?¼8XV¢*8d¤A.Xd¼<8 Fd¡n
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