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Stochastic Modeling Analysis and Applications

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International Encyclopedia of Statistical Science

The classical random flow and Newtonian mechanics are two theoretical approaches to analyze dynamic processes in biological, engineering, physical and social sciences under random perturbations. Historically, in the classical approach (Bartlett; 1969, Ross; 1971), one considers a dynamic system as a random flow or process with a certain probabilistic laws such as: diffusion, Markovian, nonmarkovian and etc. From this type consideration, one attempts to determine the state transition probability distributions/density functions (STPDF) of the random process. The determination of the unknown STPDF leads to the study of deterministic problems in the theory of ordinary or partial or integro-differential equations (Lakshmikantham and Leela 1969a, b). For example, a random flow that obeys a Markovian probabilistic law leads to

$$\begin{array}{rcl} \frac{\partial } {\partial s}P(s,x,t,B)& =& q(s,x)P(s,x,t,B) -{\int \nolimits \nolimits }_{{R}^{n}-\{x\}} \\ & & P(s,y,t,B)Q(s,x,dy),\end{array}$$
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Author information

Authors and Affiliations

  1. Chesapeake Capital Corporation, Richmond, VA, USA

    Anil G. Ladde

  2. University of South Florida, Tampa, FL, USA

    Gangaram S. Ladde

Authors
  1. Anil G. Ladde
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  2. Gangaram S. Ladde
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Editor information

Editors and Affiliations

  1. Department of Statistics and Informatics, Faculty of Economics, University of Kragujevac, City of Kragujevac, Serbia

    Miodrag Lovric

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Ladde, A.G., Ladde, G.S. (2011). Stochastic Modeling Analysis and Applications. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_571

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