3
votes
1answer
62 views

Solving a recurrence for a random walk revisited

I previously asked about the following recurrence which I get when trying to solve a random walk problem given a positive integer $x$. $p_i = \dfrac{p_{i-1}}{2} + \dfrac{p_{i+2}}{2}$ if $0< i < ...
4
votes
1answer
73 views

Recurrence for random walk

I have the following recurrence which I get when trying to solve a random walk problem given a positive integer $x$. $p_i = \dfrac{p_{i-1}}{2} + \dfrac{p_{i+2}}{2}$ if $0< i < x$ $p_i = 1$ if ...
1
vote
1answer
136 views

How to solve recurrence in two variables

How can you solve this simple looking recurrence relation in two variables? $f(a,b) = 1 + \frac{a f(a+1,b+1) + (x-a)f(a+1,b)}{x}$ The function $f$ is defined for non-negative integer values $a$ and ...
3
votes
1answer
129 views

A difference equation related to RW on Hypercube

I am trying to solve the following recurrent relation $$ T(n)=\frac{n}{m}T(n-1)+\frac{m-n}{m}T(n+1)+1, \,\, \text{subject to } T(m)=0 $$ Where $0\leq n\leq m$ and $m$ is a fixed integer. I have ...