L10 - Brownian Motion (Wiener Process)

L10 Brownian - 600mm Make“(Wiener?mc€$S 3" k “9&5 h Mot-’8‘ M GEHNI‘M a Ftfidcs cusyeahd M 4‘053 H can be Jam{bu a «bud 44

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Unformatted text preview: 600mm Make“ (Wiener ?mc€$S) 3" k “9&5 h Mot-’8‘ M: GEHNI‘M a; Ftfidcs cusyeahd. M 4‘053. H can be Jam-{bu a; «bud- 44. ‘59. RN we‘ihiwnl EM? ConsiAer angina cf of. he, 5M6. :\ PM so we: «on 3%,, haytens «2A0 M5 Mm}; .fnskaé a; \. Ms.) M. Ma», 4 5m? an my amp a Lxsrlfi: .mkd4 I. Thea, X“) = A1- ( x,+x‘+...+x ,. a] 3 what Xizf-H uf’lz -' "r’lz 1m, ijm] g o Var(X£b\) = (bur. L5; " To 36’ «Mmmeuee, ~0— wnl Id brawl—a: a erxm) é' 0’1: "(6:2 Moreen? :: v Z = "(I ._‘.. ’ JT r=n {— M M, N“) NJ c—L-IPNWCOI‘) =a xm ~ dU‘(o, w‘) “in: {Kcfihh has “Hernia? W13 uh xc+)—x(s)m(o,m>u‘) A190, Mine gal-ks 9!. Xle) we enhances Mms4 4:. as A Nimr Recess {WM} 37am pooceSS samfamg BI. ?(wm=o)=l :5 a Conmms‘fihe’ CMHAUGB is?!) $7.. {mu} in: MM W3 «~in “(‘3‘WCSM N‘CO, w‘lt-fl) B3. Smfle Fri-ks 05. {Wit-)3 m Mamas M 1:. way») i: I’mperfies 0% ‘Nf’: ‘3 Second ~or<hr cManciv-zzafim WC.) :0 [Mex = Ehm] .1: E[W(e)—W(ofl = o lutan $ R" (sit) I: C" (STE) by N‘Co, 051-) s<b v—i 0‘, (mg), “ca—wcmwm] = var (NCQ) + cov (Wis),WC-t)—W(s)) 'L a W-S w EI‘NM] -E [ma-mu] 3"_'—" W =0 :0 5 “NA S<‘L’ ’5 KW (at) = cw = off MM(SI+) =P k “0+ (085 , M: can?“ Wi—H b q “3:53d Yousan ?Nce55 , fiLg=NaLfit “M , ,4“ («A = 2mm = sinufi-M: c o Cfi (5.1:) = CM (at) = A MMCMA I2} the. m my”: 9+“ We) «a Km» mme mm m- kriloh‘on- Mi) .1: “I: f Nth) , 7n}. 4 M W dun. PmB- a} M Wm} dumb 3m Hm .‘s cm ,»o+mv.m.+ n- amm is k» ,Mmm is Me. n m . 03: A a? {mm :5 canal a 640mm mm .1 3‘» M3 m 4, 3M9“ hugs g so , we have (xc+,3,xc+,3,...,mn)) SOMHE‘ Gaussron tandem von‘aHes . a} w? iwmh a; q 6mm“ Poocess. R5919: (wcs,),m+,),_,wu,.)) are, \Mr unbmkons J, W Gauser mm wrouas : mt.) , mm mm ,wcm-wcm, ...,wcsn\-war) 3) Aflhooak mas—3 :; “dram: eve/flaws, H- is «Nahum»: “Wm L..- .mo M an. ms. sum), ‘IeAr, m gamiwé éefiVoKV‘b a), q W? 15 fine. Me. mm incess. ...
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This note was uploaded on 03/18/2012 for the course ECE 805 taught by Professor Eryilmaz during the Spring '12 term at Ohio State.

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L10 Brownian - 600mm Make“(Wiener?mc€$S 3" k “9&5 h Mot-’8‘ M GEHNI‘M a Ftfidcs cusyeahd M 4‘053 H can be Jam{bu a «bud 44

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