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Results tagged with stochastic-processes
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user 141969
A stochastic process is a collection of random variables usually indexed by a totally ordered set.
3
votes
3
answers
139
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Expected time till extinction in a B&D process
This is computed based on the following recursive formula $$w_n=\frac{\lambda_nw_{n+1}+\mu_nw_{n-1}+1}{\lambda_n+\mu_n}$$ where: $n$ is the inital state, State $0$ is absorbing, $\lambda_n$ and $\mu_n …
- 419
0
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Expected time till extinction in a B&D process
A solution for $w_i$ can be built directly by defining $$\delta_i=w_{i+1}-w_i$$ where $\delta_i$ is clearly the expected time to reach State $i$ (for the first time) from State $i+1$.
We then need to …
- 419
1
vote
1
answer
158
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Computing probability of ultimate absorption in B&D processes
Consider a B&D process with infinitely many states, State 0 absorbing. Probability of ultimate absorption when starting in State $n$ (denoted $a_n$) is computed by solving $$a_n=\frac{\lambda_na_{n+1} …
- 419