# Tagged Questions

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### Linear Algebra Stochastic Matrix and Markov Chains

I have a few true and false questions I need help with. Can someone please check my work? The product of two stochastic matrices is a stochastic matrix. This is false I found a counterexample. 2 ...
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### Positive definitness of infinite dimensional matrices

Assume $M=(b_{i,j})_{ i,j=1}^{\infty}$ is an infinite dimensional matrix such that $b_{i,i}>0$ and $b_{i,j}=b_{j,i}$ for all $i,j\in\mathbb{N}$ (i.e., $M$ is symmetric with positive diagonal ...
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### Absorption probability in 1D RW with asymmetric step sizes, $x<0$

What is the probability of absorption at $0$, as a function of position $x$, for a 1D random walk (on $\mathbb{Z}$) with asymmetric step sizes? For example, suppose that you can take two steps ...
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### Proof that the square of a stochastic matrix is stochastic

We know that the square of a stochastic matrix is also stochastic, because the two-step transition matrix of a Markov chain is necessarily stochastic. However, in there another way to independently ...
### How to find $X_i$ from this equation
Suppose $X_i=\nu_i+\frac{m-i}{m}X_{i+1}+\frac{i}{m}X_{i-1},\quad 1\le i\le m$ where $X_0=X_{m+1}=0$. I need to find an expression for $X_i$ in terms of $v_i$, $i$, and $m$. I know how to find it ...