XI, 529 p. 136 illus., 61 illus. in color. online resource
SUMMARY
Uncertainty is an inherent feature of both properties of physical systems and the inputs to these systems that needs to be quantified for cost effective and reliable designs. The states of these systems satisfy equations with random entries, referred to as stochastic equations, so that they are random functions of time and/or space. The solution of stochastic equations poses notable technical difficulties that are frequently circumvented by heuristic assumptions at the expense of accuracy and rigor. The main objective of Stochastic Systems is to promoting the development of accurate and efficient methods for solving stochastic equations and to foster interactions between engineers, scientists, and mathematicians. To achieve these objectives Stochastic Systems presents: ยทย ย ย ย ย ย ย ย A clear and brief review of essential concepts on probability theory, random functions, stochastic calculus, Monte Carlo simulation, and functional analysis ย ยทย ย ย ย ย ย ย ย ย Probabilistic models for random variables and functions needed to formulate stochastic equations describing realistic problems in engineering and applied sciences ย ยทย ย ย ย ย ย ย ย ย Practical methods for quantifying the uncertain parameters in the definition of stochastic equations, solving approximately these equations, and assessing the accuracy of approximate solutions ย Stochastic Systems provides key information for researchers, graduate students, and engineers who are interested in the formulation and solution of stochastic problems encountered in a broad range of disciplines. Numerous examples are used to clarify and illustrate theoretical concepts and methods for solving stochastic equations. The extensive bibliography and index at the end of the book constitute an ideal resource for both theoreticians and practitioners
CONTENT
Probability Essentials -- Random Functions -- Probabilistic Models -- Stochastic Integrals and Itรด's Formula -- Properties of Solutions of Stochastic Equations -- Stochastic Equations with Small Uncertainty -- Stochastic Algebraic Equations -- Stochastic Differential Equations with Deterministic Coefficients -- Stochastic Differential Equations with Random Coefficients
SUBJECT
Engineering
Distribution (Probability theory)
Engineering mathematics
System safety
Engineering
Quality Control
Reliability
Safety and Risk
Probability Theory and Stochastic Processes
Appl.Mathematics/Computational Methods of Engineering
