# markov-process's questions - Chinese 1answer

1.246 markov-process questions.

### 2 Properties of Discrete Time Continuous State Markov Process

I have a problem setup that reduces to finding the stationary state of a discrete time continuous state stationary Markov process. Is that state unique, as it is in the discrete state case? ...

### Questions about Markov process usage

I've read the answer of George Lowther on this question and I don't understand his proof. I know just a few things on Markov Process. If I define $\left(X_n\right)_{n \in \mathbb{N}}$ with $X_0=1$ and ...

### Find out whether the two statements about a stochastic process are equivalent

Let $\xi_t$, $t \in \mathbb{R}$ be a stochastic process, and $\mathcal{F}_{=t}$, $\mathcal{F}_{\geq t}$, $\ldots$ are $\sigma$-algebras induced by it. I want to find out whether the two following ...

### 1 If $i$ is recurrent then expected recurrence time is the limit of $\frac 1 {(1-s)p_{ii}(s)}$

Theorem: i is recurrent then $\mu_{ii}=\sum_{n=1}^\infty nf_{ii}^n = \lim_{s\rightarrow 1^{-}} \frac 1 {(1-s)p_{ii}(s)}$ Proof: Let $i$ be recurrent. Then, note: \begin{align} & \lim_{s\...

### 1 Communication between states i and j implies equality of periodicity of i and j

Claim:$i\leftrightarrow j$ implies $d\left ( i \right )=d\left ( j \right )$ Suppose $i\leftrightarrow j$: This implies that j is accessible from i and i is accessible from j. Then, $\exists n_{1}$ ...