# Questions tagged [markov-process]

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 processes.

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### Poisson: Conditional Probability on Pizza order

I am not sure about my answer. In particular, part b of the following question. Pizza orders arrive according to a Poisson process of rate 20 per hour. Orders are independently for a vegetarian ...
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### Proof of strong Markov Property of double sided Levy Process

Let $(X_t)_{t\in\mathbb{R}}$ be a Levy Process, i.e. $X_0 = 0$ a.s., $X$ has independent and stationary increments, and almost all paths $t\mapsto X_t(\omega)$ are right continuous with left hand ...
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### A Continuous-Time Markov Process Taking All Possible Values

Let $\mathbb{N}$ be the set of positive integers. For each $n \in \mathbb{N}$, let $X^{(n)}=\{ X^{(n)}(t): t \geq 0 \}$ be a Markov chain with state-space the two point set $\{0,1\}$ and $Q$-matrix \...
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### Why are coordinate processes introduced?

I don't fully understand what a coordinate process is and why they are used. My lecture notes say the following: For an arbitrary measurable space $(S,\mathcal{S})$ we denote by $S^{[0,\infty)}$ ...
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