STOCHASTIC VERSUS DETERMINISTIC SYSTEMS ITERATIVE PROCESSES

Continuous state dynamic models can be reformulated into discrete state processes. This process generates numerical schemes that lead theoretical iterative schemes. This type of method of stochastic modelling generates three basic problems. First, the fundamental properties of solution, namely, existence, uniqueness, measurability, continuous dependence on system parameters depend on mode of convergence. Second, the basic probabilistic and statistical properties, namely, the behavior of mean, variance, moments of solutions are described as qualitative/quantitative properties of solution process. We observe that the nature of probability distribution or density functions possess the qualitative/quantitative properties of iterative prosses as a special case. Finally, deterministic versus stochastic modelling of dynamic processes is to what extent the stochastic mathematical model differs from the corresponding deterministic model in the absence of random disturbances or fluctuations and uncertainties.

Most literature in this subject was developed in the 1950s, and focused on the theory of systems of continuous and discrete-time deterministic; however, continuous-time and its approximation schemes of stochastic differential equations faced the solutions outlined above and made slow progress in developing problems. This monograph addresses these problems by presenting an account of stochastic versus deterministic issues in discrete state dynamic systems in a systematic and unified way.

Contents:

• Stochastic Systems of Difference Equations with Random Parameters Methods
• Stochastic Systems of Difference Equations of Ito-Type-Methods
• Stochastic Systems of Difference Equations: Qualitative Analysis
• Random Polynomials
• Numerical Schemes for Systems of Differential Equations with Random Parameters
• Numerical Schemes for Systems of Difference Equations of Ito-Type
• Discrete-Time Probabilistic, Stochastic Dynamic Modeling and Statistical Data Analyses
• Appendices:
  • Stochastic
  • Ordinary Differential Equations with Random Parameters
  • Boundary Value Problems

Readership: The monograph can be used as a reference book for experimental and applied scientists working with stochastic and deterministic difference equations for modelling and data analysis or the mathematical modelling of continuous, discrete and state dynamic processes. It is particularly useful for those in engineering sciences, interdisciplinary researchers, mathematics, and statistics. It can also used as a textbook for a 'Special Topics' graduate course.