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In probability theory, a piecewise-deterministic Markov process (PDMP) is a process whose behaviour is governed by random jumps at points in time, but whose evolution is deterministically governed by an ordinary differential equation between those times. The class of models is "wide enough to include as special cases virtually all the non-diffusion models of applied probability." The process is defined by three quantities: the flow, the jump rate, and the transition measure.
In mathematics, a continuous-time random walk (CTRW) is a generalization of a random walk where the wandering particle waits for a random time between jumps. It is a stochastic jump process with arbitrary distributions of jump lengths and waiting times. More generally it can be seen to be a special case of a Markov renewal process.
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References
- ↑ Singwi, K.; Sjölander, A. (1960). "Resonance Absorption of Nuclear Gamma Rays and the Dynamics of Atomic Motions". Physical Review. 120 (4): 1093. doi:10.1103/PhysRev.120.1093.
- ↑ Chudley, C. T.; Elliott, R. J. (1961). "Neutron Scattering from a Liquid on a Jump Diffusion Model". Proceedings of the Physical Society. 77 (2): 353. doi:10.1088/0370-1328/77/2/319.
- ↑ Sears, V. F. (1966). "Theory of Cold Neutron Scattering by Homonuclear Diatomic Liquids: I. Free Rotation". Canadian Journal of Physics. 44 (6): 1279–1297. doi:10.1139/p66-108.
- ↑ Sears, V. F. (1967). "Cold Neutron Scattering by Molecular Liquids: Iii. Methane". Canadian Journal of Physics. 45 (2): 237–254. doi:10.1139/p67-025.
- ↑ Hall, P. L.; Ross, D. K. (1981). "Incoherent neutron scattering functions for random jump diffusion in bounded and infinite media". Molecular Physics. 42 (3): 673. doi:10.1080/00268978100100521.
- ↑ Merton, R. C. (1976). "Option pricing when underlying stock returns are discontinuous". Journal of Financial Economics . 3 (1–2): 125–144. doi:10.1016/0304-405X(76)90022-2. hdl: 1721.1/1899 .
- ↑ Christensen, H. L. (2012). "Forecasting high-frequency futures returns using online Langevin dynamics". IEEE Journal of Selected Topics in Signal Processing . 6 (4): 366–380. doi:10.1109/JSTSP.2012.2191532. hdl: 10.1109/JSTSP.2012.2191532 .
- ↑ Grenander, U.; Miller, M.I. (1994). "Representations of Knowledge in Complex Systems". Journal of the Royal Statistical Society, Series B. 56 (4): 549–603. JSTOR 2346184.
