Search results
Results from the WOW.Com Content Network
A result is called "deep" if its proof requires concepts and methods that are advanced beyond the concepts needed to formulate the result. For example, the prime number theorem — originally proved using techniques of complex analysis — was once thought to be a deep result until elementary proofs were found. [1]
In stochastic analysis a random process is a predictable process if it is possible to know the next state from the present time. The branch of mathematics known as Chaos Theory focuses on the behavior of systems that are highly sensitive to initial conditions. It suggests that a small change in an initial condition can completely alter the ...
Any predictable change or pattern in a time series that recurs or repeats over a one-year period can be said to be seasonal. It is common in many situations – such as grocery store [27] or even in a Medical Examiner's office [28] —that the demand depends on the day of the week. In such situations, the forecasting procedure calculates the ...
Also called infinitesimal calculus A foundation of calculus, first developed in the 17th century, that makes use of infinitesimal numbers. Calculus of moving surfaces an extension of the theory of tensor calculus to include deforming manifolds. Calculus of variations the field dedicated to maximizing or minimizing functionals. It used to be called functional calculus. Catastrophe theory a ...
In mathematics, a metric space is a set where a notion of distance (called a metric) between elements of the set is defined. Much of analysis happens in some metric space; the most commonly used are the real line, the complex plane, Euclidean space, other vector spaces, and the integers.
The systems studied in chaos theory are deterministic. If the initial state were known exactly, then the future state of such a system could theoretically be predicted. However, in practice, knowledge about the future state is limited by the precision with which the initial state can be measured, and chaotic systems are characterized by a strong dependence on the initial condit
This can be used to show that the gambler's total gain or loss varies roughly between plus or minus the square root of the number of games of coin flipping played. de Moivre 's martingale: Suppose the coin toss outcomes are unfair , i.e., biased, with probability p of coming up heads and probability q = 1 − p of tails.
In stochastic analysis, a part of the mathematical theory of probability, a predictable process is a stochastic process whose value is knowable at a prior time. The predictable processes form the smallest class that is closed under taking limits of sequences and contains all adapted left-continuous processes.