Ornstein–Uhlenbeck process

The Ornstein-Uhlenbeck process is like a game of tag. Imagine two people moving around a room. One person is 'it' and trying to catch the other. The other person is running away but they can't run away too fast. If they run too fast they will slow down and the person who is 'it' can catch them. This means they have to find a balance between running away quickly and slowing down to make sure they don't run away too fast. Now imagine this happening in a room where the floor and walls are curved, so it's like a bowl. The two people are constantly trying to find the right balance, but they can never escape the room. That's the Ornstein-Uhlenbeck process. It's a mathematical equation to model how some types of random movements happen over time.