All Questions
Tagged with markov-chains real-analysis
3 questions
2
votes
0
answers
103
views
Find a function $f\geq 0$ such that $e^{-t[(x-\partial_x)\partial_x]^2} f$ is not non-negative for some $t\geq 0$
Consider the square of the Ornstein-Uhlenbeck operator $$A=[(x-\partial_x)\partial_x]^2=(x-\partial_x)\partial_x (x-\partial_x)\partial_x.$$ We know that $[(x-\partial_x)\partial_x]^2$ cannot be a ...
- 90
6
votes
1
answer
256
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Perron-Frobenius and Markov chains on countable state space
The following question naturally arises in the theory of Markov chains with countable state space to which I would be curious to know the answer:
Let $A:\ell^1 \rightarrow \ell^1$ be a contraction, i....
- 173
1
vote
0
answers
99
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How is the dominated convergence theorem applied in the proof of Lyapunov’s criterion?
Let $$\Gamma(f,g):=\frac12f'g'\;\;\;\text{for }f,g\in C^1(\mathbb R),$$ $\mu$ be a probability measure on $(\mathbb R,\mathcal B(\mathbb R))$ with a continuously differentiable and positive density $\...
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