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Tagged with fa.functional-analysis stochastic-processes
157 questions
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A question about positive operator pregenerator [closed]
Thank you for reading.
My question was raised up when I tried to prove an example in the book of Liggett(1985), which is in P13 Example 2.3(a).
Here is a link of the page:
https://books.google.com/...
- 385
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Equivalent Definitions of Gaussian Process?
The Gaussian process $\{X_t\}_{t \in T}$ ($T=[0,1]$ for example) is usually defined using its finite-dimensional distribution. I came across this statement many times: linear operator (not necessarily ...
- 103
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criterions for polar set of Feller processes
Suppose $X_t$ is the solution to
$$
d X_t=b(X_t)dt+dL_t,\quad X_0=x.
$$
where $L$ is a rotational symmetric $\alpha-$stable process with $\alpha\in (0,1]$, $b$ is Lipchitz.
Assume $\Gamma\subseteq ...
- 515
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252
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Hadamard product (Schur product) in $L^2[0,1]$
Let's consider the separable Hilbert space $\mathcal{H} = L^2[0,1]$ of square-integrable functions on the interval $[0,1]$ with orthonormal basis $(e_j)$. For $x,y \in \mathcal{H}$, the Hadamard ...
- 195
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Some problems about symmetric convolution semigroup on the unit circle
These are problems from Example 1.4.2 of Fukushima's book "Dirichlet forms and symmetric Markov processes".
Let $\Lambda$ be the set of all real sequences $\left\{\lambda_n\right\}_{n\in\mathbf{Z}}$ ...
- 369
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322
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Comparison of Parameter estimation using maximum likelihood and Maximum entropy
I am not sure if the question is appropriate but I want to try my luck. One can estimate a parameter using maximum likelihood and we know it is optimal. On the other hand there are methods which uses ...
- 495
-1
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Approximation of function in general measure space
Let $\mu$ be a $\sigma$-finite measure on $R^n$ ($n\geq 1$) and $(E,d)$ be a complete metric space. For any measurable function $f: R^n\to E$ with
$$
\int_{R^n}d(f(x),f(x_0))\mu(dx)<\infty,\quad \...
- 411