y**y
发帖数: 25 | 1 the problem is like
B(t) is a standard brownian motion,
what is the probability that B reaches b before hiting -a?
I know this kind of problem could be solved by martingale stopping time
thereom.
But I wonder if it still could be done by transition probability density(tpd
).
Since we know the tpd of B(t) is N(0,t),so we could calculate
P(-a
then I don't know how to continue to get the solution of my problem.
by limit(t=inf) or integrate t from 0 to inf?
or even the whole | J******d
发帖数: 506 | 2 这个问题被问过很多遍了。
最直接的解法是Martingale Stopping Time。如果把a, b换成整数，初等概率论的办法
也能解出来(e.g. a=1, b=2), 然后就轻易推广到一般情形。
tpd
【在 y**y 的大作中提到】
: the problem is like
: B(t) is a standard brownian motion,
: what is the probability that B reaches b before hiting -a?
: I know this kind of problem could be solved by martingale stopping time
: thereom.
: But I wonder if it still could be done by transition probability density(tpd
: ).
: Since we know the tpd of B(t) is N(0,t),so we could calculate
: P(-a: then I don't know how to continue to get the solution of my problem.
| y**y
发帖数: 25 | 3 how to solve it using basic probability method supposing a=1, b=2?
please enlightening me...3x!!!
。如果把a, b换成整数，初等概率论的办法
也能解出来(e.g. a=1, b=2), 然后就轻易推广到一般情形。
【在 J******d 的大作中提到】
: 这个问题被问过很多遍了。
: 最直接的解法是Martingale Stopping Time。如果把a, b换成整数，初等概率论的办法
: 也能解出来(e.g. a=1, b=2), 然后就轻易推广到一般情形。
:
: tpd
| J******d
发帖数: 506 | 4 走到1停和-1停的概率相等.
走到-1的话,再走到1停的概率和走到-2停的概率,就相当于
从0开始走到-2停的概率或走到1停的概率,即为题目所求.
而这两个概率相加必为1. 列个方程一算就出来了, 还是线性的.
【在 y**y 的大作中提到】
: how to solve it using basic probability method supposing a=1, b=2?
: please enlightening me...3x!!!
:
: 。如果把a, b换成整数，初等概率论的办法
: 也能解出来(e.g. a=1, b=2), 然后就轻易推广到一般情形。
| s****r
发帖数: 94 | 5 reflection principle?
【在 y**y 的大作中提到】
: how to solve it using basic probability method supposing a=1, b=2?
: please enlightening me...3x!!!
:
: 。如果把a, b换成整数，初等概率论的办法
: 也能解出来(e.g. a=1, b=2), 然后就轻易推广到一般情形。
|
|
