scholarly journals Time Series, Stochastic Processes and Completeness of Quantum Theory

2011 ◽  
Author(s):  
Marian Kupczynski
Keyword(s):  
Time Series ◽  
Quantum Theory ◽  
Stochastic Processes

scholarly journals Probability in quantum mechanics

1982 ◽  
Vol 5 (1) ◽  
pp. 183-194
Author(s):  
J. G. Gilson
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Stochastic Processes ◽  
Probability Density ◽  
Fluid Theory ◽  
Standing Problem

By using a fluid theory which is an alternative to quantum theory but from which the latter can be deduced exactly, the long-standing problem of how quantum mechanics is related to stochastic processes is studied. It can be seen how the Schrödinger probability density has a relationship to time spent on small sections of an orbit, just as the probability density has in some classical contexts.

Basic Fourier series

1979 ◽  
Vol 369 (1736) ◽  
pp. 115-136 ◽  
Keyword(s):  
Time Series ◽  
Fourier Series ◽  
Stochastic Processes ◽  
Numerical Approximation ◽  
Basic Number ◽  
Second Order ◽  
Orthogonal Functions ◽  
Sturm Liouville

The concept of basic number is applied to the development of a simple analogue of the Sturm–Liouville system of the second order. This is then employed to deduce a family of q -orthogonal functions, which leads to a generalization of the Fourier and Fourier–Bessel expansions. The numerical approximation of basic integrals is discussed and some aspects of the evaluation of C a (q; x) are mentioned. A few of the zeros of this function are listed, and, in conclusion, an indication is given of the possibility of applying the analysis presented in this paper to thé study of stochastic processes and time-series.

scholarly journals A METHOD FOR INFERRING HIERARCHICAL DYNAMICS IN STOCHASTIC PROCESSES

2008 ◽  
Vol 11 (01) ◽  
pp. 1-16 ◽  
Author(s):  
OLOF GÖRNERUP ◽  
MARTIN NILSSON JACOBI
Keyword(s):  
Time Series ◽  
Stochastic Processes ◽  
A Priori ◽  
Main Idea ◽  
A Priori Knowledge ◽  
Finite State Automaton ◽  
State Spaces ◽  
Markovian Dynamics ◽  
Finite State ◽  
Operational Algorithm

Complex systems may often be characterized by their hierarchical dynamics. In this paper we present a method and an operational algorithm that automatically infer this property in a broad range of systems — discrete stochastic processes. The main idea is to systematically explore the set of projections from the state space of a process to smaller state spaces, and to determine which of the projections impose Markovian dynamics on the coarser level. These projections, which we call Markov projections, then constitute the hierarchical dynamics of the system. The algorithm operates on time series or other statistics, so a priori knowledge of the intrinsic workings of a system is not required in order to determine its hierarchical dynamics. We illustrate the method by applying it to two simple processes — a finite state automaton and an iterated map.

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