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visits member for 2 years, 9 months
seen Mar 14 '13 at 16:37

Nov
2
awarded  Teacher
Nov
1
answered A ruler with missing graduation.
May
10
comment What do ideals of a ring say about its inner structure?
Could you give an example of a property of a ring not following from its ideals but only from its modules?
May
7
comment What do ideals of a ring say about its inner structure?
If there's a non-trivial ideal $I$ in a ring, then for any $x\in I$, $x$ does not have an inverse? Otherwise, $I$ would cover the whole ring.
May
7
awarded  Supporter
May
7
asked What do ideals of a ring say about its inner structure?
Oct
26
comment From a deterministic discrete process to a Markov chain: conditions?
I was thinking about the explanation how to obtain a probabilistic process from a deterministic process (3rd paragraph in your post). As you said, given a deterministic process $a_t=F(a_{t-1})$, we make it probabilistic by making $a_0$ a random variable. If $a_0$ is fixed, we get only a degenerate chain with prob's 0/1. However, how about keep $a_0$ fixed, consider the chain homogenous and let the transition probabilities be the average over many deterministic transitions? (e.g., if the deterministic chain goes from $s_0$ to $s_1$ 1/3 times over many steps, $p(s_1|s_0):=\frac{1}{3}$)
Oct
25
awarded  Editor
Oct
25
revised From a deterministic discrete process to a Markov chain: conditions?
added 648 characters in body
Oct
25
comment From a deterministic discrete process to a Markov chain: conditions?
However, my question remains: in what case would this yield a M. process (under the assumption that $a_0$ follows some starting distribution)? You said that its's not likely to produce a Markov process, but is there a Theorem that confirms this? Otherwise, there must be some conditions on the "abstraction" function and the process? I'm looking for some references or book?
Oct
25
comment From a deterministic discrete process to a Markov chain: conditions?
@Dider: thanks! As you and Craig pointed out example #1 was not good (gives a degenerate process which is not interesting). As you said, what I had in mind is that $a_0$ follows some starting distribution and then we obtain a random process.
Oct
25
comment From a deterministic discrete process to a Markov chain: conditions?
Thanks, but I don't think this answers the question. It wasn't about whether the deterministic process is a Markov chain or not (it was about whether the resulting probabilistic process is a Markov chain or not).
Oct
25
awarded  Student
Oct
25
asked From a deterministic discrete process to a Markov chain: conditions?