Dear experts,

I have below put a brief discussion of my understanding, but could not manage to get a complete overview. Kindly help me understand.

Below I have put my understanding in my own words based on the content from the book mentioned above.

Below I would like to discuss and seek clarifications primarily on Compound Poisson Process.

Before that, I have below, put briefly my understating on Simple Poisson process and then move to Compound Poisson Process.

In the below diagram, the jumps are of uniform size one (or one step). Here jumps appear to be strictly positive.

Here RV are termed as S1, S2,…Sn (so countably finite)

11.3.1 Construction of Compound Poisson Process:

N(t) be a Poisson process with intensity λ

Let Y1, Y2… be a sequence of identically distributed random variables with mean with β = E[Yi]

I have below put a brief discussion of my understanding, but could not manage to get a complete overview. Kindly help me understand.

Below I have put my understanding in my own words based on the content from the book mentioned above.

Below I would like to discuss and seek clarifications primarily on Compound Poisson Process.

Before that, I have below, put briefly my understating on Simple Poisson process and then move to Compound Poisson Process.

__Simple Poisson Process:__In the below diagram, the jumps are of uniform size one (or one step). Here jumps appear to be strictly positive.

Here RV are termed as S1, S2,…Sn (so countably finite)

11.3.1 Construction of Compound Poisson Process:

**have random jump sizes**__Compound Poisson processes__N(t) be a Poisson process with intensity λ

Let Y1, Y2… be a sequence of identically distributed random variables with mean with β = E[Yi]