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A stochastic process is a collection of random variables usually indexed by a totally ordered set.
4
votes
1
answer
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When are time changes of Feller-Dynkin processes still Feller-Dynkin processes?
A Markov process $X_t$ on $E$ is a Feller-Dynkin (or sometimes just Feller) process if its semigroup is a strongly continuous, sub-Markov semigroup $\{P_t:t\geq 0\}$ of linear operators on $C_0(E)$ (m …
6
votes
1
answer
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When is $\mathbf{E}^{x}[f(X_t)]$ a continuous function of $x$?
Let $E$ be a locally compact Hausdorff space with countable base and $X_t$ be a stochastic process taking values in the one-point compactification of $E$ (with the Borel $\sigma$-algebra). Let $f$ be …
1
vote
Diffusion processes in probabilistic modelling
You might look at the introduction of Bernt Oskendal's Stochastic Differential Equations. He gives seven motivating problems (at least he does in the edition I have) for studying stochastic calculus. …
12
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2
answers
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Gluing Markov processes
I am looking for a reference on the gluing together of strong Markov processes to get a new one.
Here is an example of what I have in mind. Let $B^1, B^2, \ldots $ be independent one-dimensional Bro …