Timeline for Introduction to Markov process: How to prove that a process is Markov? Part 1
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Sep 28, 2015 at 16:37 | comment | added | Did | "Can you outline the steps to show that the chaotic map generates r.v which forms markov chain?" I already did. Perhaps you are missing the point but every deterministic sequence $(x_n)$ such that $x_{n+1}=M(x_n)$ for some function $M$ is a (very degenerate) Markov chain. Proof: Look up the definitions. | |
| Sep 28, 2015 at 0:11 | comment | added | Ria George | How to show that K(x) is a dirac mass? Is it needed to show this in order to prove that the sequence output from the chaotic map is a Markov chain? Can you outline the steps to show that the chaotic map generates r.v which forms markov chain? | |
| Sep 27, 2015 at 21:21 | comment | added | Did | "can you provide links where I can find more information?" More information about what? "how to show what is a Dirac mass" One does not "show what is a Dirac mass", either one reads the definition to know what is a Dirac mass or one shows that something is a Dirac mass. For your information, the Dirac mass at $y$ is the unique measure $\mu$ such that $\mu(A)=1$ for every $A$ such that $y\in A$ and $\mu(A)=0$ for every $A$ such that $y\notin A$. | |
| Sep 27, 2015 at 21:13 | comment | added | Ria George | Thank you for your answer, can you provide links where I can find more information? I am not aware of this proof and how to show what is a Dirac mass and hence the proof. | |
| Sep 26, 2015 at 15:01 | comment | added | Did | Indeed the sequence is a Markov chain, but a very special one since its transition kernel $$K(x,A):=P(x_{n+1}\in A\mid x_n=x,x_{n-1},\ldots,x_0)$$ is such that, for every $x$, $K(x,\ )$ is a Dirac mass (at $M(x)$). Not your typical Markov chain, but a Markov chain yes. | |
| Sep 19, 2015 at 16:49 | history | edited | Ria George | CC BY-SA 3.0 |
edited title
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| Sep 19, 2015 at 16:48 | vote | accept | Ria George | ||
| S Sep 18, 2015 at 9:41 | history | suggested | Dawny33 | CC BY-SA 3.0 |
Fixed hyperlinks
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| Sep 18, 2015 at 9:21 | answer | added | RUser4512 | timeline score: 3 | |
| Sep 18, 2015 at 8:08 | review | Suggested edits | |||
| S Sep 18, 2015 at 9:41 | |||||
| Sep 18, 2015 at 7:29 | history | asked | Ria George | CC BY-SA 3.0 |