Publisher's Synopsis
In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a collection of random variables. Historically, the random variables were associated with or indexed by a set of numbers, usually viewed as points in time, giving the interpretation of a stochastic process representing numerical values of some system randomly changing over time. When interpreted as time, if the index set of a stochastic process has a finite or countable number of elements, such as a finite set of numbers, the set of integers, or the natural numbers, then the stochastic process is said to be in discrete time. If the index set is some interval of the real line, then time is said to be continuous. The two types of stochastic processes are respectively referred to as discrete-time and continuous-time stochastic processes. Discrete-time stochastic processes are considered easier to study because continuous-time processes re¬quire more advanced mathematical techniques and knowledge, particularly due to the index set being uncountable. If the index set is the integers, or some subset of them, then the stochastic process can also be called a random sequence. Stochastic processes have played a significant role in various engineering dis¬ciplines like power systems, robotics, automotive technology, signal processing, manufacturing systems, semiconductor manufacturing, communication networks, wireless networks etc. Among the above engi-neering applications of stochastic processes, we plan to concentrate on communication networks where there is lot of current interest. This will form the second part of the thematic program. For one, connections come in and leave randomly. Another area where stochastic processes have important applications is in the area of neuroscience. Applications and the study of phenomena have in turn inspired the proposal of new stochastic processes. Examples of such stochastic processes include the Wiener process or Brownian motion process, used by Louis Bachelier to study price changes on the Paris Bourse, and the Poisson pro¬cess, used by A.K. Erlang to study the number phone calls occurring in a certain period of time. These two stochastic processes are considered the most important and central in the theory of stochastic processes. Encyclopaedia of Stochastic Modeling and Control brings together research on the theory and applications of stochastic processes. It is concerned with a broad spectrum of mathematical, scientific and engineering interests. In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a collection of random variables. Historically, the random variables were associated with or indexed by a set of numbers, usually viewed as points in time, giving the interpretation of a stochastic process representing numerical values of some system randomly changing over time. When interpreted as time, if the index set of a stochastic process has a finite or countable number of elements, such as a finite set of numbers, the set of integers, or the natural numbers, then the stochastic process is said to be in discrete time. If the index set is some interval of the real line, then time is said to be continuous. The two types of stochastic processes are respectively referred to as discrete-time and continuous-time stochastic processes. Discrete-time stochastic processes are considered easier to study because continuous-time processes re¬quire more advanced mathematical techniques and knowledge, particularly due to the index set being uncountable. If the index set is the integers, or some subset of them, then the stochastic process can also be called a random sequence. Stochastic processes have played a significant role in various engineering dis¬ciplines like power systems, robotics, automotive technology, signal processing, manufacturing systems, semiconductor manufacturing, communication networks, wireless networks etc. Among the above engi-neering applications of stochastic processes, we plan to concentrate on communication networks where there is lot of current interest. This will form the second part of the thematic program. For one, connections come in and leave randomly. Another area where stochastic processes have important applications is in the area of neuroscience. Applications and the study of phenomena have in turn inspired the proposal of new stochastic processes. Examples of such stochastic processes include the Wiener process or Brownian motion process, used by Louis Bachelier to study price changes on the Paris Bourse, and the Poisson pro¬cess, used by A.K. Erlang to study the number phone calls occurring in a certain period of time. These two stochastic processes are considered the most important and central in the theory of stochastic processes. Encyclopaedia of Stochastic Modeling and Control brings together research on the theory and applications of stochastic processes. It is concerned with a broad spectrum of mathematical, scientific and engineering interests.
