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This sparked my curiosity. A little googling gives this: http://www.stat.cmu.edu/~cshalizi/754/notes/lecture-09.pdf. On page 5 they discuss your question. If you make the filtration coarser, the M …

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 …

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 …

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. …

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 …

I posted this on mathstackexchange to no avail. It is well-known (see for instance Oskendal's text) that if $T>0$ and $$b(\cdot,\cdot): [0,T] \times \mathbb{R}^n \rightarrow \mathbb{R}^n~~~~~~\sigma( …