Talk:Renewal theory

message: The example at the end uses 't' both for the general time and for the time when to replace the machines. One should use two different letters.
84.188.212.189 13:15, 30 March 2007 (UTC)
thread_title:  The example at the end 

message: I remember that in my Stats class, we used (quite a bit)
long-term average reward rate = E[W1]/E[T1]
where W1,W2,... are the rewards and T1,T2,... are the time intervals.
Is this too detail specific, or should it be added?
In any case, I can't add it because I'm not at all proficient at writing math on Wikipedia.
Akshayaj 21:11, 18 July 2007 (UTC)
replies: text: Sounds like now is a good time to learn! Just edit the page, look at how other people have achieved it, and use copy and paste. reetep 07:57, 19 July 2007 (UTC)
replies: text: Whew, didn't wreck anything.  I put the math in for the Renewal Reward result, though I did it by memory, so please check.  Feel free to change or do whatever with it Akshayaj 21:50, 19 July 2007 (UTC)
replies: text: Looks good to me - thanks for the contribution. You may find the math help page useful. reetep 11:54, 20 July 2007 (UTC)
replies: text: I had to change the Renewal Reward Theorem from 1/E[W1] back to E[W1]/E[S1].  Ths result makes a lot more sense then 1/E[W1] (that makes me almost sure this is right).  If someone thinks it's wrong, please post on the talk page as to why Akshayaj 18:46, 27 July 2007 (UTC)
thread_title: Should we mention the elementary renewal theory result for Reward-Renweal Processes?

message: I don't think, in the term 
 X_t = \sum^{\infty}_{n=1} \mathbb{I}_{\{J_n \leq t\}}=\sup \left\{\, n: J_n \leq t\, \right\},
\mathbb{I} is defined anywere...
:I was wondering the same thing. Anyone?? watson (talk) 00:06, 23 September 2010 (UTC)
replies: text: I expect it's the Indicator function --mcld (talk) 18:27, 4 October 2011 (UTC)
thread_title:  Formal Defination 

message: Is there a reason these two articles should be kept separate? Seems to me that regenerative processes aren't distinct enough to have a separate page... Closed Limelike Curves (talk) 03:42, 26 September 2023 (UTC)
replies: text: the current article Regenerative process (a topic I've never studied) indicates that renewal processes are a special case of regenerative processes. Renewal processes (as defined in this article; these I am familiar with) have a state space of \mathbb{N} and only ever progress 0\to 1\to 2\to 3\to \cdots, where each progression step is i.i.d. But Reflected Brownian motion has a state space \mathbb{R}^n_+. I can picture non-renewal regenerative processes in \mathbb{R}^n where the idea would be that no matter where your particle is its direction of travel is i.i.d.The main point of renewal theory is the results you get about laws of large numbers, but I don't know that such laws have to apply to all regenerative processes. I think this is also why we assume renewal distributions have finite mean but no such assumption has to be made for regenerative processes.If my understanding is correct then I wouldn't support a merge. — Bilorv (talk) 20:29, 1 October 2023 (UTC)
replies: text: @Closed Limelike Curves I agree with @Bilorv that the notion of regenerative process is more general than that of regenerative process. As a result, I don't think merging the two articles would make sense, and I will remove the banner from the article. Cheers, Malparti (talk) 02:08, 11 February 2024 (UTC)
thread_title:  Merge from Regenerative process