# Steady state probability needed using Markov chain

After applying v=vP\mathbf{v}=\mathbf{vP} (in a Markov chain scenario) I have following set of linear equations p0,0v0+pN,0vN=v0p_{0,0}v_0+p_{N,0}v_N=v_0 p0,1v0+p1,1v1+pN+1,1vN+1=v1p_{0,1}v_0+p_{1,1}v_1+p_{N+1,1}v_{N+1}=v_1 ⋯\cdots pk−1,kvk−1+pk,k+1vk+pN+k,kvN+k=vkp_{k-1,k}v_{k-1}+p_{k,k+1}v_k+p_{N+k,k}v_{N+k}=v_k
⋯\cdots where NN is some constant greater than 00. Further, it is known that pk,k+pk,k+1=1if k