IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Markov processes
A stochastic process {X_t} has a discrete state space and a continuous time set. Which description of the process is correct?
A process with a discrete state space and a continuous time set is a continuous-time, discrete-state process, and the Poisson counting process is the standard example because it takes integer values and can change at any real time.
- ADiscrete-time, discrete-state process, such as a simple random walk
- BContinuous-time, discrete-state process, such as a Poisson counting processCorrect
- CDiscrete-time, continuous-state process, such as an AR(1) series
- DContinuous-time, continuous-state process, such as a Poisson counting process
- Continuous-time, continuous-state process, such as a no-claims-discount (NCD) Markov chain
Explanation
Discrete state space with continuous time defines a continuous-time, discrete-state process. A Poisson counting process takes integer values and is observed at all times t≥0. The other options mislabel either the time set or the state space.
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