౷ܭֶ࣮ફϫʔΫϒοΫ ୈষ֬཰աఔͷجૅ QͷЏJ ͷ෼෍Λಋग़͢Δ 4BUPBLJ/PHVDIJ

ЏJͷઃఆ εi = Bti − Bti−1 B = (Bt )t≥0 0 = t0 < t1 < ⋯ < tn = t = 1 [0,1] tk = k n (k = 0,1,⋯, n) (εi )i=1,…,n Λ ʹ෼ׂ͢Δɻ ͓Αͼ ͱ͢Δͱɺ ͸ϒϥ΢ϯӡಈͷఆٛʹΑΓಠཱʹ N(μ/n, σ2/n) ʹै͏ɻ ϒϥ΢ϯӡಈ ʹͯɺ

ЏJͷ෼෍Λಋग़ ೚ҙͷ 0 ≤ t < t + h ʹରͯ͠ɺ Xt+h − Xt ͷ෼෍͸ Xh − X0 ͷ෼෍ͱಉҰͰ͋Δ εi = Bti − Bti−1 ͷ෼෍͸ ͜͜Ͱ Bt ∼ N(μt, σ2t) ΑΓ B1 n ͷ෼෍͸ N(μ/n, σ2/n) ͱͳΔɻ B1 n − B0 = B1 n − 0 = B1 n ti − ti−1 = (i/n) − (i − 1)/n = 1/n t0 = 0 Bt0 = B0 = 0 ͷ෼෍ͱಉҰͰ͋Δ Ͱ͋Δ͔Βɺ εi = Bti − Bti−1 ैͬͯɺ ͷ෼෍͸ N(μ/n, σ2/n) ͱͳΔɻ εi = Bti − Bti−1 ࣍ʹɺ ·ͣɺ ͸ޓ͍ʹಠཱͰ͋Δɻ ϒϥ΢ϯӡಈͷੑ࣭͔Β ఆৗ૿෼ੑ ಠཱ૿෼ੑ Xt0 =0 , Xt1 − Xt0 , Xt2 − Xt1 , ⋯, Xtn − Xtn−1 ͨͪ͸ޓ͍ʹಠཱͰ͋Δ