simulation

[Rahul-Ahuja]

I did not quite understand the topic of simulation in Markov chain and Markov jump chapters.

matrix generator of HSD as follows

-0.5 0.4 0.1
0.6 -0.8 0.2
0 0 0

Please help me with lines below.
The first step is to simulate the states occupied by the Markov jump chains.
Row 1 of the transition matrix is the conditional distribution of X1 given that X0 = H.
We use Monte Carlo simulation to generate a simulated value for X1.

If the simulated value is D, then the simulation of the sample path is complete because of the process never leaves state D. If the simulated value is S, then we use row 2 of thetransition matrix, which is the conditional distribution of X2 given that X1 = S, to simulate a value for X2.
This process is repeated to simulate additional values of the Markov jump chain.



Also kindly explain the topic of simulation in a general way.


Thank you.

 

[Calum]

When you're asking for help, it is easier if you make it clear exactly what you do and don't understand - the question you've asked requires a textbook to answer if interpreted literally!

So to try to narrow it down-

- do you understand what a transition matrix represents?
- if you do, do you understand how you could use this to simulate a transition from one state to another?
- Could you then put these together to simulate a process from start to finish?

To answer your last question, the point of simulation is that you can simulate the process over and over again, and use the results to answer questions about the process: for example, what is the distribution of the time the life spends in the sick state? And what if the transition matrix is a set of spline functions dependent on t?