Timeline for Laplace transform of sum of random variables in first hitting time problem
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Oct 10, 2020 at 18:23 | comment | added | Mateusz Kwaśnicki | I suppose Chapter 14 of Feller's An Introduction to Probability Theory and Its Applications, vol. 2 is a standard reference. | |
| Oct 10, 2020 at 14:42 | comment | added | user36706 | Thank you a million! That really clarifies the intuition. Just one more question: is there any specific rule for applying Laplace transform to summation like this, or is there any decent textbook about this topic where I can find similar problem? (You are welcomed to make it as a complete answer too...) | |
| Oct 10, 2020 at 14:29 | comment | added | Mateusz Kwaśnicki | Wait first, then toss a coin. $T$ has exponential distribution with parameter $\mu+\theta$, only after waiting for $T$ units of time the particle decides where to go. | |
| Oct 10, 2020 at 14:27 | comment | added | user36706 | @MateuszKwaśnicki: I think you may be right. I am just still wondering: with probability $\frac{\mu}{\mu + \theta}$, will $T$ remain to follow $exp(\mu+\theta)$, or would that be the case we KNOW that it would go to state $n+1$ and $T$ should be following $exp(\mu)$ now? | |
| S Oct 10, 2020 at 14:19 | history | suggested | gmvh | CC BY-SA 4.0 |
Improved formatting, added top-level tag
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| Oct 10, 2020 at 14:07 | comment | added | Mateusz Kwaśnicki | If I understand correctly, with probability $\mu/(\mu+\theta)$, $T_n$ is equal in law to $T + T_{n+1}$, and otherwise it is equal to $T + T_{n-1}$, with $T$, $T_{n-1}$ and $T_{n+1}$ independent. Is that correct? | |
| Oct 10, 2020 at 14:04 | review | Suggested edits | |||
| S Oct 10, 2020 at 14:19 | |||||
| Oct 10, 2020 at 13:43 | review | First posts | |||
| Oct 10, 2020 at 14:04 | |||||
| Oct 10, 2020 at 13:42 | history | asked | user36706 | CC BY-SA 4.0 |