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31, 21% 24, 17% 8, 5% 23, 16% 24, 16% 91, 62% 19, 13% 39, 27% 33, 23% 73 48 57 51 31 1 9 13.0% 7.4% 5.3% 12.5% 17.1% 13.2% 17.9% 4.5% 36.4% 56.5% 40.7% 36.8% 50.0% 67.1% 56.3% 65.8% 75.0% 26.0% 37.0%

2 DI 28 7 1 37 28 4 18 27 11 21 5 2 26 4 5 1 15 2 25 3 35 4 17 7 5 48 76 31 47 17 2 92 12 2 2 4 6 8 1 12 1 2 4 1 12 13 18 19 3 42 57 57 1 2 3 4 5 6 1 1 1 3 4 4 5 5 5.5 1 1.5 2 2.5 3 3.5 4 4.5 5

37 27.0% 26 19.0% 74 54.0% 9 6.4% 13 9.2% 28 19.9% 26 18.4% 37 26.2%. 24 17.0% 99 69 75 59 39 1 6 4.5% 1.4% 7.7% 2.9% 25.0% 17.9% 20.8% 50.0% 41.7% 47.0% 51.4% 54.3% 61.5% 57.1% 55.6% 42.4% 50.0% 58.3%

chap9.dvi

9 AR (i) (ii) MA (iii) (iv) (v) 9.1 2 1 AR 1 9.1.1 S S y j = (α i + β i j) D ij + η j, η j = ρ S η j S + ε j (j =1,,T) (1) i=1 {ε j } i.i.d(,σ 2 ) η j (j ) D ij j i S 1 S =1 D ij =1 S>1 S =4 (1) y j =

Black-Scholes [1] Nelson [2] Schrödinger 1 Black Scholes [1] Black-Scholes Nelson [2][3][4] Schrödinger Nelson Parisi Wu [5] Nelson Parisi-W

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42 3 u = (37) MeV/c 2 (3.4) [1] u amu m p m n [1] m H [2] m p = (4) MeV/c 2 = (13) u m n = (4) MeV/c 2 =

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1 (1) () (3) I 0 3 I I d θ = L () dt θ L L θ I d θ = L = κθ (3) dt κ T I T = π κ (4) T I κ κ κ L l a θ L r δr δl L θ ϕ ϕ = rθ (5) l

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1 Jensen et al.[6] GRT S&P500 GRT RT GRT Kiriu and Hibiki[8] Jensen et al.[6] GRT 3 GRT Generalized Recovery Theorem (Jensen et al.[6])

Generalized Recovery Theorem Ross[11] Recovery Theorem(RT) RT forward looking Kiriu and Hibiki[8] Generalized Recovery Theorem(GRT) Jensen et al.[6] GRT RT Kiriu and Hibiki[8] 1 backward looking forward

cm λ λ = h/p p ( ) λ = cm E pc [ev] 2.2 quark lepton u d c s t b e 1 3e electric charge e color charge red blue green qq

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研究シリーズ第40号

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chap10.dvi

. q {y j } I( ( L y j =Δy j = u j = C l ε j l = C(L ε j, {ε j } i.i.d.(,i q ( l= y O p ( {u j } q {C l } A l C l