Nonequilibrium statistical thermodynamics of second‐order stochastic processes in the limit of large resistance

1985 ◽  
Vol 26 (3) ◽  
pp. 505-513 ◽  
Author(s):  
B. H. Lavenda ◽  
R. Serra
Keyword(s):  
Stochastic Processes ◽  
Statistical Thermodynamics ◽  
Second Order ◽  
Nonequilibrium Statistical Thermodynamics

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.

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