Continuous-Time Markov Chain Interview Guide
Continuous-time Markov chain interview guide for states, transition rates, holding times, generator intuition, examples, and assumptions.
Candidates seeing rates, jumps, and process modeling prompts.
Continuous-time chains jump at random times
A continuous-time Markov chain moves between states, but transitions occur after random holding times rather than fixed discrete steps.
Rates replace one-step probabilities
Transition rates describe how quickly the process jumps from one state to another. The total rate out of a state determines the holding-time distribution in standard setups.
Concrete example
A queue length can be a continuous-time chain if arrivals and services happen at random times, moving the state up or down by one.
Generator intuition helps
The generator matrix stores transition rates and diagonal exit rates. It plays a role similar to the transition matrix, but for continuous time.
Common mistakes
Candidates often use discrete transition probabilities when the prompt gives rates. State whether time advances in steps or continuously before solving.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.