Timeline for Are the densities of a continuous stochastic process locally positive in time?
Current License: CC BY-SA 4.0
7 events
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| Aug 28, 2020 at 11:22 | comment | added | fsp-b | Thank you, @IosifPinelis. | |
| Aug 28, 2020 at 2:23 | comment | added | Iosif Pinelis | I think diffusions like this should cause no problems. However, as the example at mathoverflow.net/questions/370159/… shows, distributions can be however close to one another without any closeness of the corresponding densities. So, without any experience in such modeling, I'd guess it's better to avoid using broad classes of densities in modeling, and instead use integral characteristics such as cdf's and/or moments. | |
| Aug 27, 2020 at 21:13 | comment | added | fsp-b | @IosifPinelis Sorry to bother you with this extremely ill-defined question, but would you "feel" from your experience that imposing a given process $X$ to satisfy all of the above is a very restrictive model assumption if $X$ were to model a "generic data stream" (say ECG data or stock prices)? (The continuity of the density would be satisfied at least for some "reasonably-sized" class of time-homogeneous diffusions with continuously distributed initial value.) | |
| Aug 26, 2020 at 15:07 | comment | added | Iosif Pinelis | The answer at mathoverflow.net/questions/370159/… and discussion there show that your desired condition may not hold even when $X_t$ is however smooth in $t$, pathwise and on an average. So, I think no essentially non-tautological condition will suffice here. | |
| Aug 26, 2020 at 15:03 | history | edited | fsp-b | CC BY-SA 4.0 |
added 16 characters in body
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| Aug 26, 2020 at 14:56 | history | edited | fsp-b | CC BY-SA 4.0 |
edited title
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| Aug 26, 2020 at 14:48 | history | asked | fsp-b | CC BY-SA 4.0 |