Non-equilibrium theory of the allele frequency spectrum ... - ICMS
Non-equilibrium theory of the allele frequency spectrum ... - ICMS
Non-equilibrium theory of the allele frequency spectrum ... - ICMS
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Finding <strong>the</strong> boundary condition – continuedIf (B t ) t≥0 is a standard Brownian motion and T := inf{t ≥ 0 :B t = 0}, <strong>the</strong>n∫ ∞limy↓0 0P y {B s ∈ dy, T > s}dy∫ ∞ 1ds = lim √ − √ 1 e −(2y)2 /2s dsy↓0 0 2πs 2πs= 2y.By Itô–McKean <strong><strong>the</strong>ory</strong>,∫θ ∞2 limy↓0 0Q ↓ s(y, dy)dyds = θ limy↓0yb(y) .
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