l********e
发帖数: 349 | 1 都是精华区里看到的题目，但是没有找到满意的解答，求助高手。
1.A drunken man is on a 100 meter long bridge at the 17 meter position. He
has a
50% chance of staggering forward and backward one meter per step. What is
the
probability he will make it to the end of the bridge before the beginning?
Assume he takes one step per second, how long is he going to stay on the
bridge?
精华区里给出一个PARTIAL ANSWER，觉得不是很理想，递推公式的导出不是很容易
我第一个想法是用STOPPING TIME、HITTING TIME 去做这个题目，哪位大大有办法给个
简洁明了的SOLUTION。
2. Solve dy_t = dt + y dw_t
Solution: y_t=\i |
t*****l
发帖数: 805 | 2 第二道题目 你可以设 x=x1*x2
dx1=x1 dw (easy to find the solution)
dx2=a(t)dt+b(t)dw,(you can find b(t)=0)
dx=d(x1 x2)=x1 dx2+x2 dx1+ dx1 dx2
then you can find the form of a(t) in terms of x1, and the solution
to x2 is just a regular differential equation. |
l********e
发帖数: 349 | 3 The first step assumption x=x1*x2 is most important here. Any particular
reasons to set up it like this?
I will try this form of solution next time when I fail in a general
geometric BM. Thanks anyway.
Any thoughts about the other problems, guys? |
J****x
发帖数: 37 | 4 3. It is not possible, since the covariance matrix is not semi-positive-
definite (one eigenvalue -0.0487 is negatvie). |
