Jump diffusion is a stochastic process that involves jumps and diffusion. It has important applications in condensed matter physics and in option pricing.
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:
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.
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