Hawkes Processes are a type of stochastic process used in statistics and probability theory. They are named after their creator, Alan Hawkes, who first introduced them in 1971.

Hawkes Processes are used to model events that occur randomly over time. These processes are particularly useful in modeling phenomena that exhibit clustering behavior, as they are able to capture the dependency between events.

In a Hawkes Process, each event generates a series of subsequent events, known as the excitation process. The excitation process is modeled by a triggering kernel, which determines the probability of a new event occurring at a given time, based on the history of past events.

One of the key features of Hawkes Processes is their ability to model self-exciting behavior. This means that an initial event can trigger a cascade of subsequent events, leading to a burst of activity. This makes Hawkes Processes particularly useful in applications such as finance, where sudden spikes in trading activity can have significant impact on market dynamics.

Overall, Hawkes Processes provide a powerful framework for modeling stochastic events and their dependencies over time. Whether you are analyzing financial data, studying the spread of disease, or modeling social networks, Hawkes Processes offer a flexible and robust approach for understanding the dynamics of complex systems.