Question

有关概率论与随机过程的 随机过程中的布朗运动的证明步骤?

Answer 1

W(t)是布朗运动

W(t+a)-W(a)服从正态分布 N(0,t)

For example:

X(t)-X(0)= W(t+a)-W(a) N(0,t)

Moreover:

X(t+k)-X(k)=W(t+k+a)-W(a)-{W(k+a)-W(a)}=W(t+k+a)-W(k+a) N(0,t+k+a-k-a)~N(0,t) and is independ of k

Y(t+k)-Y(k)=aW((t+k)/a^2)-aW(k/a^2)~a(N(0,t/a^2))~N(0,t),is also independent of k

Y is also brownian motion