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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.

Compétences : Mathématiques

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Concernant l'employeur :
( 0 commentaires ) London, United Kingdom

N° du projet : #1655888

6 freelance ont fait une offre moyenne de 22 £ pour ce travail

VolKa

See PM,please.

20 £ GBP en 1 jour
(53 Commentaires)
5.5
ethicalboy

I can do this.

20 £ GBP en 1 jour
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RotorProgrammer

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

20 £ GBP en 2 jours
(7 Commentaires)
3.9
adobrinevski

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 Plus

30 £ GBP en 2 jours
(1 Commentaire)
1.9
Seepre

I am ready to do this.

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amit1freelancer

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

20 £ GBP en 3 jours
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