Conventional PSM Frames

  • Octavian Iordache
Part of the Understanding Complex Systems book series (UCS, volume 70)


The polystochastic models, PSMs, are conceptual tools designed to analyze and manage multi-level complex systems.

PSMs characterize systems emerging when several stochastic processes occurring at different conditioning levels, interact with each other, resulting in qualitatively new processes and systems. The capabilities of random systems with complete connections, RSCC are outlined. The real field frame, developed to enclose multi-level modeling confronts over-parameterization problems.

Examples pertaining to the domains of chemical engineering and material science include mixing in turbulent flow and diffusion on hierarchical spaces.

The challenges of different views for the same phenomenon are pointed out.


Markov Chain Cayley Tree Ultrametric Space Random Evolution Illustrative Case Study 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Cohen, J.E.: Long-run Growth Rates of discrete multiplicative processes in Markovian environments. Journal Math. Anal. and Appl. 69, 243–251 (1979a)zbMATHCrossRefGoogle Scholar
  2. Cohen, J.E.: Random evolutions in discrete and continuous time. Stochastic Proc. Applications 9, 245–251 (1979b)zbMATHCrossRefGoogle Scholar
  3. Iordache, O.: Polystochastic Models in Chemical Engineering. VNU-Science Press, Utrecht (1987)Google Scholar
  4. Iosifescu, M., Grigorescu, S.: Dependence with complete connections and applications. Cambridge Univ. Press, Cambridge (1990)zbMATHGoogle Scholar
  5. Krambeck, F.J., Shinnar, R., Katz, S.: Interpretation of tracer experiments in systems with fluctuating throughput. Ind. Engng. Chem. Fundam. 8, 431–444 (1968)CrossRefGoogle Scholar
  6. Ogielski, A.T., Stein, D.L.: Dynamics of ultrametric spaces. Physical Review Letters 55, 1634–1637 (1985)CrossRefMathSciNetGoogle Scholar
  7. Paladin, G., Mézard, M., De Dominicis, C.: Diffusion in an ultrametric space: a simple case. J. Physique Lett. 46, 1985–1989 (1985)CrossRefGoogle Scholar
  8. Pruscha, H.: Learning models with continuous time parameter and multivariate point processes. J. Appl. Probab. 20, 884–890 (1983)zbMATHCrossRefMathSciNetGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2011

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  • Octavian Iordache

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