All Questions
Tagged with stochastic-processes fa.functional-analysis
157 questions
4
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Choice of predictable (or jointly measurable) eigenvalues and eigenvectors of nuclear-operator-valued stochastic process
Let $q^{ij}$, $i,j\in\mathbb{N}$, be predictable real-valued stochastic processes. Let $(e^i)$, $i\in\mathbb{N}$ be an ONB of a separable Hilbert space $H$. Assume that $Q=\sum_{i,j=1}^\infty q^{ij}...
CommunityBot
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votes
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Does infinite-dimensional Brownian motion live in hyperplanes?
I'll begin this question with the finite-dimensional case, as a
warmup.
Let me say a continuous path $\omega : [0,1] \to \mathbb{R}^d$ is
hyperplanar if there exists a nonzero $x \in \mathbb{R}^d$ ...
- 29.8k
18
votes
1
answer
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Existance of certain almost invariant functions related to amenability and piece-wise transformations
We would like very much to know the answer to the following question:
Let $\|\cdot\|$ be any norm on $\mathbb{Z}^d$ and let $W(\mathbb{Z}^d)$ be the group of all bijections of $\mathbb{Z}^d$ such ...
- 4,705
4
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0
answers
1k
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The spectrum of a Markov Operator and Invariant Measures
Suppose I have a discrete-time Markov Chain (in an infinite dimensional state space $\Omega$) with Markov operator $P$, a linear operator on the space of bounded measurable functions on $\Omega$. (Or ...
- 509
12
votes
3
answers
3k
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Infinitesimal generators of stochastic processes
What's the $L^1$ analogue of Stone's theorem saying that any strongly continuous 1-parameter unitary groups has a unique self-adjoint generator?
More precisely: let $X$ be a measure space ($\sigma$-...
- 1,068
11
votes
1
answer
642
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Random walk origin return monotinicity
Consider a Markov chain on $\mathbb{Z}^d$ with transition kernel $P$ for adjacent vertices (non-diagonal). Essentially this is a $d$ dimensional random walk with the probability of a transition ...
- 17k
5
votes
1
answer
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Does generator of continuous time random walk map heat kernel from L^2 to L^2?
Let $\Gamma = (G,E)$ be an undirected, infinite, connected graph with no multiple edges or loops. We equip $\Gamma$ with a set of edge weights $\pi_{xy}$, where, given $e=\{x,y\}\in E$, we write $\...
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