Continuous-time Markov process
A continuous-time Markov process is like a very long game of "hot potato" where a group of people pass a potato to each other randomly, but in a special way. At any given time, the potato is in someone's possession, and they can keep it for a while or pass it to someone else. But the person who receives the potato also has to pass it to someone else, and the time they keep it before passing it on is random.
The rules of the game depend on what has happened in the past. For example, if someone just passed the potato to you, you are more likely to pass it on quickly because you don't want to get stuck with it for too long. The process of passing the potato around follows a pattern of probabilities that depend only on the current state of the game and not on the past or future.
In a continuous-time Markov process, the game is played continuously, without stops or breaks. Instead of playing for a certain number of rounds, you play forever, passing the potato back and forth minute by minute, second by second, or even faster.
Markov processes are used in many fields, such as physics, chemistry, biology, economics, and finance, to model how systems evolve over time. In a continuous-time Markov process, you can use mathematical formulas to predict how the potato will move around and how long each person will hold onto it.
The rules of the game depend on what has happened in the past. For example, if someone just passed the potato to you, you are more likely to pass it on quickly because you don't want to get stuck with it for too long. The process of passing the potato around follows a pattern of probabilities that depend only on the current state of the game and not on the past or future.
In a continuous-time Markov process, the game is played continuously, without stops or breaks. Instead of playing for a certain number of rounds, you play forever, passing the potato back and forth minute by minute, second by second, or even faster.
Markov processes are used in many fields, such as physics, chemistry, biology, economics, and finance, to model how systems evolve over time. In a continuous-time Markov process, you can use mathematical formulas to predict how the potato will move around and how long each person will hold onto it.