Piecewise-deterministic Markov process
A piecewise-deterministic Markov process is like playing a game. There are certain points when the game stops and a new set of rules is used. Each time you play the game, you start from the beginning but with different rules.
Imagine you are playing a game where you are a bird flying through the sky. The rules of the game change every time you reach a cloud. Sometimes you can fly straight through the cloud, and sometimes you bounce off the cloud and have to change direction. You don't know what will happen until you reach the cloud, but you know that the rules will change.
The same thing happens with the piecewise-deterministic Markov process. It's a mathematical model that has different rules at different times. The rules change when certain events happen, like when the process hits a certain value or reaches a specific point in time.
The process is called "Markov" because the rules for what happens next only depend on the current state of the process. It's called "piecewise-deterministic" because the rules are deterministic (meaning there is a fixed outcome for each set of inputs), but only apply to certain pieces of time or specific values.
So, to summarize: a piecewise-deterministic Markov process is like playing a game where the rules change at certain times or values, but the outcome of each move is determined by the previous move.
Imagine you are playing a game where you are a bird flying through the sky. The rules of the game change every time you reach a cloud. Sometimes you can fly straight through the cloud, and sometimes you bounce off the cloud and have to change direction. You don't know what will happen until you reach the cloud, but you know that the rules will change.
The same thing happens with the piecewise-deterministic Markov process. It's a mathematical model that has different rules at different times. The rules change when certain events happen, like when the process hits a certain value or reaches a specific point in time.
The process is called "Markov" because the rules for what happens next only depend on the current state of the process. It's called "piecewise-deterministic" because the rules are deterministic (meaning there is a fixed outcome for each set of inputs), but only apply to certain pieces of time or specific values.
So, to summarize: a piecewise-deterministic Markov process is like playing a game where the rules change at certain times or values, but the outcome of each move is determined by the previous move.