Talk:Continuous-time random walk

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a reference is wished

“The Wiener process is the standard example of a continuous time random walk in which the waiting times are exponential and the jumps are continuous and normally distributed.”

Can some one give a reference here? especially about the fact waiting times are exponential. Thanks — Preceding unsigned comment added by 2606:A000:1018:8132:28BC:FA3A:52B3:D6ED (talk) 01:29, 28 December 2016 (UTC)

I think this is wrong. If the waiting time is exponential, there will be a finite jumps during a give period, but the sample functions of Wiener process has infinite many details. — Preceding unsigned comment added by 2606:A000:1018:8132:10BE:75F8:749E:198E (talk) 20:04, 9 January 2017 (UTC)

This is definitely incorrect, a CTRW is related to a Wiener process in the diffusive limit where the length scale of the jumps and the time scale of the waiting time are both taken to zero. The CTRW is not itself a Wiener process. — Preceding unsigned comment added by 129.94.8.106 (talk) 23:39, 29 June 2017 (UTC)

I've deleted the Wiener process "example" and added the homogeneous Poisson point process, which does fit the definition in the article. If anyone wants to expand the section to include something with a non-trivial (perhaps symmetric) increment distribution, that would be even better. The difference of two Poisson point processes with the same rate parameter, perhaps. 148.88.169.158 (talk) 10:07, 24 May 2019 (UTC)

Clarification of differences to Wiener process and Brownian motion

Would it be worth clarifying, perhaps in the introductory paragraph, that a continuous time random walk is not the same as Brownian motion, or the Wiener process? This may be obvious to most people but some people (like me) might land here while looking for this other related process. Probably best if someone with more statistical background makes this edit. Billtubbs (talk) 18:33, 3 April 2022 (UTC)