Jump diffusion
Jump diffusion is a stochastic process that involves jumps and diffusion. It has important applications in magnetic reconnection, coronal mass ejections, condensed matter physics and in option pricing.
In physics
In crystals, atomic diffusion typically consists of jumps between vacant lattice sites. On time and length scales that average over many single jumps, the net motion of the jumping atoms can be described as regular diffusion.
Jump diffusion can be studied on a microscopic scale by inelastic neutron scattering and by Mößbauer spectroscopy. Closed expressions for the autocorrelation function have been derived for several jump(-diffusion) models:
Singwi, Sjölander 1960: alternation between oscillatory motion and directed motion
Chudley, Elliott 1961: jumps on a lattice
Sears 1966, 1967: jump diffusion of rotational degrees of freedom
Hall, Ross 1981: jump diffusion within a restricted volume
In economics and finance
In option pricing, a jump-diffusion model is a form of mixture model, mixing a jump process and a diffusion process. Jump-diffusion models have been introduced by Robert C. Merton as an extension of jump models. Due to their computational tractability, the special case of a basic affine jump diffusion is popular for some credit risk and short-rate models.