All Questions
8 questions
1
vote
1
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143
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Comparison of hitting probability of two Markov chains both with only one absorbing state version 2 under stronger condition
Let $N_n:=\{1,2,\cdots,n\}$. Given two finite states Markov chains $\big(X^{(j)}_i\in N_n\}\big)_{i=0}^\infty$ for $j\in\{1,2\}$, both of which have two absorbing states at $1$ and $n$.
$\text{Pr}\...
- 2,239
8
votes
4
answers
8k
views
Is there MDPs (Markov Decision Process) which have a non deterministic optimal policy?
I'm working on Markov Decision Process and I have not found yet an example of MDP that has a stochastic (non deterministic) optimal policy. Is there MDPs that have a stochastic optimal policy or is it ...
- 254
3
votes
2
answers
264
views
Probability of one species reaching zero before the other in a Markov process on a 2d lattice
$\textbf{Background}$: Say we've got a two-variable system of stochastic chemical reactions, with quantities $\vec{x}(t) = (x_1(t),x_2(t)) \in \mathbb{N}^2$ evolving according to the following system, ...
- 41
3
votes
2
answers
973
views
How much larger than the relaxation time can the mixing time be?
The notation is mostly taken from the book "Markov chains and mixing times" by Levin, Peres, and Wilmer.
Consider an irreducible, aperiodic, time-reversible, discrete-time Markov chain on a finite ...
- 1,269
2
votes
1
answer
640
views
Reachability for Markov process
Let $X$ be a Markov process (in continuous or discrete time) and define an event
$$
R(T,A) = (\exists t\leq T: X_t \in A).
$$
I have seen in one paper that
$$
\Pr[R(\infty,A)] = \sup\limits_{\tau} \...
- 1,655
0
votes
1
answer
262
views
Construction of a Markov process with prescribed local behavior and state-dependent jump distribution
Let
$(E,\mathcal E)$ be a measurable space
$\mathcal E_b:=\left\{f:E\to\mathbb R\mid f\text{ is bounded and }\mathcal E\text{-measurable}\right\}$
$(\kappa_t)_{t\ge0}$ be a Markov semigroup on $(E,\...
- 167
0
votes
1
answer
96
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What is the significance of Blumenthal and Getoor's result on the boundedness of paths of a standard Markov process?
In the book Markov processes and Potential Theory of Blumenthal and Getoor we can find the following result:
I don't understand the significance of this result. If I don't misinterpret the assertion, ...
- 167
-1
votes
1
answer
370
views
What's the probability of two independent events in time domain?
Suppose there are two independent events A and B. The probability that A or ...
- 29