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I am trying to understand various types of stochastic processes. In order for that to happen, I needed some simple examples to be built so that I can build an intuition about them.

According to the book of Hwei Hsu (Chapter-5, Page-161, "Description of a Random Process"), I can design the following simple and intuitive examples myself using only a standard die:

2. Continuous parameter (or Continuous-time) process

???

4. Continuous-state process

Suppose, we roll a die either a finite ($n$) number of times or an infinite number of times and plot $\frac{e^{X(t)}}{1000}$ as a graph like the following:

enter image description here


My first question is: are my examples correct? If not, kindly help me to make the necessary corrections.

Secondly, what would be the example of (2)?

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