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Prob of simple random walk hitting ub/lb before lb/ub

Hi, I need an analytical solution to a problem which I believe was solved decades ago.

The problem is as following:

A particle x begins at time t=0, with a value of 0. At each time interval, t=1,2,... it is incremented by 1 with probability p, and decremented by 1 with probability q=1-p. There are two boundaries a>0 and b<0, such that when the particle hits either one it stops.

I would like to know the probability that the particle hits a (or b) before b (or a). I'd also like to have the solution with maximum intermediate steps and explanation.

In a classic text by William Feller "An Introduction to Probability Theory and its Application", this problem is discussed in full detail.

Kỹ năng: Toán học

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Về Bên Thuê:
( 0 nhận xét ) London, United Kingdom

Mã Dự Án: #1655888

6 freelancer đang chào giá trung bình £22 cho công việc này


See PM,please.

£20 GBP trong 1 ngày
(53 Đánh Giá)

I can do this.

£20 GBP trong 1 ngày
(22 Đánh Giá)

Hello. I can make necessary calculations to determine the probabilities.

£20 GBP trong 2 ngày
(7 Đánh Giá)

I am a PhD student in theoretical physics. I've worked a lot with probability theory for my research. I have a formula for the "continuous" version of your problem, where instead of a discrete random walk one takes a Thêm

£30 GBP trong 2 ngày
(1 Đánh Giá)

I am ready to do this.

£20 GBP trong 7 ngày
(0 Đánh Giá)

I can solve your new modified questions question. Electrical Engineer here with lots of experience in MATLAB

£20 GBP trong 3 ngày
(2 Đánh Giá)