Let W be a standard Brownian motion, and also a Є R and ẞ Є R. (a) For a given smooth function 9 : R→ R, assume that the function ƒ : R+ × (0, ∞) → R satisfies f(0,x) = g(x) for x = R, as well as af af (T,x) Ξα -(T, x) + Эт მე B² a²ƒ 2 0x2 (T,x), for (T,x) Є R+ × R. Show that f(t, x)=E[g(x+at+BW₁)], for (t, x) = R4 × R.
Let W be a standard Brownian motion, and also a Є R and ẞ Є R. (a) For a given smooth function 9 : R→ R, assume that the function ƒ : R+ × (0, ∞) → R satisfies f(0,x) = g(x) for x = R, as well as af af (T,x) Ξα -(T, x) + Эт მე B² a²ƒ 2 0x2 (T,x), for (T,x) Є R+ × R. Show that f(t, x)=E[g(x+at+BW₁)], for (t, x) = R4 × R.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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