Timeline for Continuity of sample paths of stochastic processes
Current License: CC BY-SA 3.0
5 events
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| Jul 9, 2012 at 4:34 | comment | added | S. Carnahan♦ | lpdbw, having created a new account, wrote the following in an answer: `Thanks for your answer. In fact, I did't claim this was a "research level" problem. All I wanted was a convenient reference suitable for citation since I could not find one.' | |
| Jul 8, 2012 at 17:29 | comment | added | Nate Eldredge | And the second property guarantees that this extension is a modification of the original process. | |
| Jul 8, 2012 at 17:29 | comment | added | Nate Eldredge | I don't think this question is really research-level. I think if you read the proof (which Google Books will not show me) you will find that it goes through for a general complete metric space. You might find a more explicit statement in another textbook, but this fact seems sufficiently simple that one wouldn't really need to give a reference. Note that the first property says that, almost surely, $X_s$ is uniformly continuous on $S \cap [0,k]$ for every $k$. Hence it has a unique continuous extension to all of $\mathbb{R}$. | |
| Jul 8, 2012 at 9:35 | history | edited | lpdbw | CC BY-SA 3.0 |
deleted 2 characters in body
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| Jul 8, 2012 at 8:38 | history | asked | lpdbw | CC BY-SA 3.0 |