Brownian bridge
A brownian bridge is like a path that a tiny little particle follows as it bounces around randomly. Imagine you have a toy car and you place it on a track. Sometimes the car goes in one direction, sometimes it goes in another direction, but it always stays on the track.
Now imagine that the car is really small and is moving around in a glass of water. The water is moving randomly, and because the tiny car is so light, it moves with the water. But even though it's moving with the water, it's still bouncing around randomly.
A brownian bridge is a way to understand how that tiny car moves around in the water. We start by imagining that the car starts at one place in the glass of water, and we want to know what the chances are that it will end up at another place in the glass of water.
To figure this out, we need to know how the car moves over time. We can measure how far the car moves in a certain amount of time, then measure how far it moves in the next amount of time, and keep doing this over and over.
Each time we measure how far the car moves, we're making a step on the brownian bridge. And the more steps we take, the closer we get to understanding how the tiny car moves in the water.
So, a brownian bridge is like a way to understand how a tiny particle moves randomly over time. We measure how far it moves in little steps, and take lots of those little steps to understand the bigger picture.
Now imagine that the car is really small and is moving around in a glass of water. The water is moving randomly, and because the tiny car is so light, it moves with the water. But even though it's moving with the water, it's still bouncing around randomly.
A brownian bridge is a way to understand how that tiny car moves around in the water. We start by imagining that the car starts at one place in the glass of water, and we want to know what the chances are that it will end up at another place in the glass of water.
To figure this out, we need to know how the car moves over time. We can measure how far the car moves in a certain amount of time, then measure how far it moves in the next amount of time, and keep doing this over and over.
Each time we measure how far the car moves, we're making a step on the brownian bridge. And the more steps we take, the closer we get to understanding how the tiny car moves in the water.
So, a brownian bridge is like a way to understand how a tiny particle moves randomly over time. We measure how far it moves in little steps, and take lots of those little steps to understand the bigger picture.