x Turn on thread page Beta
 You are Here: Home >< Maths

# A very tough Stochastic Question watch

1. Suppose we have a process X which either jumps up by 1 or down by 1 each time period, but the probability of an up-jump, given that the process is in state x, is equal to x=(x + 1).
If denotes the probability of ever hitting 0, given that the starting point is x,

show that

. Hence deduce that .

Thanks
2. Do you have the actual question? Do we know anything about the value of x (e.g. is it positive or negative)?
3. (Original post by mathsRus)
..
You seem to have some typos. Assuming the "up-jump" probability is actually supposed to be x / (x+1):

Use the same approach you'd use for a normal Gamblers Ruin (or random walk) problem to form a recurrence between and .
Try to rearrange it to form a recurrence between and . You can then use this relationship repeatedly to prove the first result (use induction if you really want to be formal).

For the final result (which I assume is supposed to be ), assume (or justify, depending on how rigourous you have to be) that . Then use the relationship you proved to find an expression for this limit in terms of h1.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: October 28, 2015
Today on TSR

### Loughborough better than Cambridge

Loughborough at number one

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams