# Poisson Process

*Quant & Pricing — Finicade finance glossary*

A Poisson process counts events that arrive randomly at a constant average rate, with waiting times that are exponentially distributed and memoryless. In finance it models things that happen suddenly rather than continuously: defaults, market jumps, order arrivals. Pairing it with a diffusion gives jump-diffusion, which explains the fat tails and short-dated smile that pure Brownian motion cannot.

**Also known as:** jump process, counting process, Poisson arrivals

**Related terms:** [Jump Diffusion](https://finicade.com/glossary/jump-diffusion), [Probability Distribution](https://finicade.com/glossary/probability-distribution), [Default](https://finicade.com/glossary/default), [Brownian Motion](https://finicade.com/glossary/brownian-motion), [Credit Risk](https://finicade.com/glossary/credit-risk)

Source: https://finicade.com/glossary/poisson-process