返回题库

布朗桥的边际分布

Brownian Bridge

专题
Finance / 金融
难度
L4

题目详情

Let BsB_{s} be a Brownian bridge, that is a Brownian motion constrained such that B0=0B_{0} = 0 and Bt=xB_{t} = x . What is the distribution of BsB_{s} , for 0≤s<t0\leq s< t ?

解析

布朗桥：给定 B0=0,Bt=xB_0=0,B_t=x。

对 0≤s<t0\le s<t，

Bs∣(Bt=x)∼N(stx, s(t−s)t).\boxed{B_s\mid(B_t=x)\sim N\left(\frac{s}{t}x,\ \frac{s(t-s)}{t}\right)}.