A stochastic process satisfying the Markov property: the distribution of the future states given the value of the current state does not depend on the past states. Use this tag for general state space processes (both discrete and continuous times); use (markov-chains) for countable state space ...

learn more… | top users | synonyms

-2
votes
2answers
190 views

Is first order moving average a Markov process?

Given first order moving average $$ x(n) = e(n) + ce(n-1) $$ where $e(n)$ is a sequence of Gaussian random variables with zero mean and unit variance which are independent of each other, and $c$ is ...
2
votes
1answer
100 views

A question about a stochastic process being Markov

Let $(X_{s},\mathcal{F}_{s})$ be a stochastic process adapted to a given filtration. I was told that, in order to prove that $X$ is Markov, it suffice to prove that for any nonnegative, ...
3
votes
1answer
701 views

Why does a time-homogeneous Markov process possess the Markov property?

Klenke defines (Definition 17.3, p. 346) a time-homogeneous Markov process independently, rather than as a special case of a stochastic process that possesses the Markov property (Definition 17.1, p. ...
1
vote
0answers
25 views

showing a condition implies convergence to invariant distribution

For an arbitrary Markov chain, I'm trying to show that $\lVert{ P_{\mu}\circ \theta_n^{-1} - \nu \rVert}\to 0$ iff $\sum_j \lvert{ P_{ij}^n - \nu(j)\rvert}\to 0$, where $\theta_n^{-1}$ is a shift ...
1
vote
2answers
64 views

Expected number of steps between states in a Markov Chain

Suppose I am given a state space $S=\{0,1,2,3\}$ with transition probability matrix $\mathbf{P}= \begin{bmatrix} \frac{2}{3} & \frac{1}{3} & 0 & 0 \\[0.3em] \frac{2}{3} ...
1
vote
1answer
38 views

makov chains and property

let $X_t$ for $t \in \{1,2,...,10\}$ be a sequence of independent tosses of a fair coin. We denote heads with 1 and tails with 0. Define the random variable $S_n=\sum_{t=1}^n X_t$ for $n \in ...
1
vote
2answers
240 views

Estimating the transition matrix given the stationary distribution

Let's say we are given a Markov chain for variable $X = [x_1, ..., x_n]$; also we are given a desired stationary distribution for this graph $P_\infty = [p_1, ..., p_n]^\top$. How can we design an ...
1
vote
1answer
114 views

Why is the following example of a Markov process not strong Markov

$X(t) := 0 \;\; (t \leq \tau),\;\; t - \tau\;\;(t \geq \tau)$ with $\tau$ exponentially distributed. Then X has the Markov property but not Strong Markov Property. But why ???? Can someone kindly ...
1
vote
0answers
70 views

“To every Q-matrix corresponds a unique Markov process.” Proving uniqueness

"To every Q-matrix corresponds a unique Markov process." I'm trying to understand Klenke's proof of the uniqueness part of this proposition. Klenke's proof Following is an adapted version of ...