Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Cohen, J.E.: Long-run Growth Rates of discrete multiplicative processes in Markovian environments. Journal Math. Anal. and Appl. 69, 243–251 (1979a)
Cohen, J.E.: Random evolutions in discrete and continuous time. Stochastic Proc. Applications 9, 245–251 (1979b)
Iordache, O.: Polystochastic Models in Chemical Engineering. VNU-Science Press, Utrecht (1987)
Iosifescu, M., Grigorescu, S.: Dependence with complete connections and applications. Cambridge Univ. Press, Cambridge (1990)
Krambeck, F.J., Shinnar, R., Katz, S.: Interpretation of tracer experiments in systems with fluctuating throughput. Ind. Engng. Chem. Fundam. 8, 431–444 (1968)
Ogielski, A.T., Stein, D.L.: Dynamics of ultrametric spaces. Physical Review Letters 55, 1634–1637 (1985)
Paladin, G., Mézard, M., De Dominicis, C.: Diffusion in an ultrametric space: a simple case. J. Physique Lett. 46, 1985–1989 (1985)
Pruscha, H.: Learning models with continuous time parameter and multivariate point processes. J. Appl. Probab. 20, 884–890 (1983)
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Iordache, O. (2011). Conventional PSM Frames. In: Modeling Multi-Level Systems. Understanding Complex Systems, vol 70. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17946-4_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-17946-4_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17945-7
Online ISBN: 978-3-642-17946-4
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)