👉 The Levy process, also known as the Lévy process, is a continuous-time stochastic process that generalizes Brownian motion by incorporating jumps. It is characterized by three key properties: continuity in probability, independent increments, and stationary and independent increments. The increments over non-overlapping intervals are independent and normally distributed, but the process can also exhibit jumps at random times, making it more flexible than Brownian motion. This flexibility allows Levy processes to model phenomena with sudden changes, such as financial market crashes or natural disasters. The Levy math involves the study of these processes through their characteristic functions, which are used to derive properties and solve problems in probability theory, finance, and other fields.
