Timeline for Finding jump probabilities from mean-occupancy values for positions on a one-dimensional random walk
Current License: CC BY-SA 2.5
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 11, 2012 at 14:07 | comment | added | mike | If you have occupancy times of a birth n' death process until hitting some particular state they are geometric, and if you put the process in continuous time they are exponential, and I think you can relate even joint occupancies to values of bessel processes via imbedding them in brownian motion & using something like a Ray-Knight theorem. | |
| Jun 12, 2010 at 22:22 | history | bounty ended | Rob Grey | ||
| Jun 5, 2010 at 21:33 | history | bounty started | Rob Grey | ||
| Jun 5, 2010 at 21:10 | history | edited | Rob Grey | CC BY-SA 2.5 |
Asked reverse formulation of question where one hopes to find solutions for jump probability assignments from mean occupancy values. Original question is preserved below new formulation.; edited body
|
| Jun 4, 2010 at 0:39 | history | edited | Rob Grey | CC BY-SA 2.5 |
Added question about finding jump probabilities from mean occupancy data; deleted 2 characters in body; edited body; added 15 characters in body
|
| Jun 3, 2010 at 23:06 | history | edited | Rob Grey | CC BY-SA 2.5 |
added 70 characters in body
|
| Jun 3, 2010 at 21:34 | comment | added | Rob Grey | Dear Steve, I updated my question to reflect my previous comment. Perhaps it will make a difference? My apologies for that. | |
| Jun 3, 2010 at 21:33 | history | edited | Rob Grey | CC BY-SA 2.5 |
Changed 'randomly assigned' to 'assigned' (see Steve Huntsman's comment & my reply)
|
| Jun 3, 2010 at 21:31 | comment | added | Rob Grey | Steve, thank you, I appreciate the link. I suppose my question though was - given a 'particular' random assignment of jump probabilities, can one do better than averaging over all the assignments from P to find the mean occupancy for a position $x_k$? Aside from the contribution of a particular initialization state, my intuition was that the mean occupancy would not be the same for all sites. | |
| Jun 3, 2010 at 20:06 | comment | added | Steve Huntsman | If so, consider a given assignment of elements of $P$. The concomitant transition matrix can be constructed straightforwardly (including a "coffin state") and the associated fundamental matrix as well ( books.google.com/… ). This will give you the information you need for that particular assignment. Then average over the assignments from $P$. | |
| Jun 3, 2010 at 20:00 | comment | added | Steve Huntsman | Is the measure on $P$ uniform? | |
| Jun 3, 2010 at 19:54 | history | asked | Rob Grey | CC BY-SA 2.5 |