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Composite stochastic processes

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  • van Kampen, N.G.

Abstract

Certain problems in physics and chemistry lead to the definition of a class of stochastic processes. Although they are not Markovian they can be treated explicitly to some extent. In particular, the probability distribution for large times can be found. It is shown to obey a master equation. This demonstrates how a non-Markovian process can be approximated on a course time scale by a Markov description. The conditions for this approximation to be valid are discussed.

Suggested Citation

  • van Kampen, N.G., 1979. "Composite stochastic processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 96(3), pages 435-453.
  • Handle: RePEc:eee:phsmap:v:96:y:1979:i:3:p:435-453
    DOI: 10.1016/0378-4371(79)90005-0
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    Citations

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    Cited by:

    1. Bezák, V., 1994. "Diffusion induced by Poissonian shocks: a concept inherent in a stochastic theory of wear," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 206(1), pages 127-148.
    2. van Kampen, N.G., 1997. "Noise in the current through a membrane," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 244(1), pages 414-425.
    3. Dekker, H., 1980. "Critical dynamics the expansion of the master equation including a critical point," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 103(1), pages 80-98.
    4. Dekker, H., 1986. "Escape over a potential barrier: The activation rate in bistable systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 135(1), pages 80-104.
    5. Dekker, H., 1991. "Multisite spin hopping analysis of multilevel dissipative quantum tunneling and coherence at finite temperatures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 178(2), pages 289-331.
    6. Dekker, H., 1980. "Critical dynamics the expansion of the master equation including a critical point," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 103(1), pages 55-79.

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