10.4 Another way to define a diffusion process is as follows. Let t; x and t; x be continuous functions of t and x, where

10.4 Another way to define a diffusion process is as follows. Let μðt; xÞ and σðt; xÞ be continuous functions of t and x, where ðt 0 E½σ2 ðu; BðuÞÞdu ,N Define XðtÞ 5 Xð0Þ 1 ðt 0 μðu; BðuÞÞdu 1 ðt 0 σðu; BðuÞÞdBðuÞ t $ 0 Then, fXðtÞ; t $ 0g is a diffusion process with μ as its drift function and σ the diffusion function. If Xð0Þ 5 x0; μðt; xÞ 5 μ and σðt; xÞ 5 σ, show that fXðtÞg is a Brownian motion with drift, where the drift is the initial state x0