yes it does Google Central limit theorem for poisson compounding the answer is on stack exchange. Best wishes, David Booth

Dear Professor Booth:

Thank you for pointing me to math.stackexchange.com . Did you mean the following question posted there:

https://math.stackexchange.com/questions/2818656/compound-poisson-distribution-central-limit-theorem-and-estimation

Although it starts with a statement which seems to be the answer to my question, it does not provide neither a proof nor the reference to the published proof.

Or did you mean a different discussion on math.stackexchange.com ?

Thank you,

A.L.

This may be of help: https://www.probabilitycourse.com/chapter11/11_1_2_basic_concepts_of_the_poisson_process.php

Yes your question is posted there . Google my suggestion to find it. The link I was thinking of is: https://mathoverflow.net/questions/169136/compound-poisson-process-and-central-limit-theorem Please note that you must read all the way to the bottom. The first posting is not the one you want. See the one that was closed as not reseachy enough.Hope this is of some help. BTW I am not an expert in this area. Best wishes, David Booth

Dear Edward G. Brown :

Thank you for providing a link to the section 11.1.2 titled "Basic Concepts of the Poisson Process" in the only theory of probability textbook. I was unable to find any reference to CLT with Poisson compounding in this section. Please clarify.

The online textbook you referenced does have a chapter on limit theorems, but I was unable to find anything about CLT with Poisson compounding in it either.

Thank you,

A.L.

Sorry Azat Latypov , it may not have what you are looking for. I was thinking that the following sections about Poisson may have done.