Fractional Brownian motion

Fractional Brownian Motion is a type of random motion that is made up of lots of small steps which can go up or down. It's like rolling a die and if it lands on one side it goes up and if it lands on the other side it goes down. The thing that makes fractional Brownian motion different is that the steps taken can be bigger or smaller depending on what happened before. If you have a long run of good luck, the steps will be bigger, but if you have a long run of bad luck, the steps will be smaller.