Regularly varying correlation functions and KMO-langevin equations

Hokkaido Mathematical Journal

Volumn 26, Issue 2, 1997, Pages 457-482

  Inoue, Akihiko ^a  

^a HOKKAIDO UNIVERSITY   (Japan)

Author keywords

Correlation function; First KMO Langevin equation; Outer function; Reflection positivity; Regular variation; Stationary process; Stationary random distribution; variation

Indexed keywords

EID: 33746208453     PISSN: 03854035     EISSN: None     Source Type: Journal    
DOI: 10.14492/hokmj/1351257978     Document Type: Article

References (21)

1. Alder B.J. and Wainwright T.E., Velocity autocorrelations for hard spheres. Phys. Rev. Lett. 18 (1967), 988-990.
2. Bingham N.H. and Teugels J.L., Mercerian and Tauberian theorems for differences. Math. Z. 170 (1980), 247-262.
3. Bingham N.H., Goldie C M. and Teugels J.L., Regular variation. Cambridge Univ. Press, Cambridge, 1987.
4. de Haan L., An Abel-Tauber theorem for Laplace transforms. J. London Math. Soc. (2) 13 (1976), 537-542.
5. Hida T., Maruyama G. and Nisio M., A Guide to Probability Theory 2. Seminar on Probability, 1962, (in Japanese).
6. Inoue A., The Alder-Wainwright effect for stationary processes with reflection positivity. J. Math. Soc. Japan 43 (1991), 515-526.
7. Inoue A., On the equations of stationary processes with divergent diffusion coefficients. J. Fac. Sci. Univ. Tokyo Sec. IA 40 (1993), 307-336.
8. Inoue A., On Abel-Tauber theorems for Fourier cosine transforms. J. Math. Anal. Appl. 196 (1995), 764-776.
9. Itô K., Stationary random distributions. Mem. Coll. Sci. Univ. Kyoto. 28 (1954), 209-223.
10. Okabe Y., On a stochastic differential equation for a stationary Gaussian process with T-positivity and the fluctuation-dissipation theorem. J. Fac. Sci. Univ. Tokyo Sec. IA 28 (1981), 169-213.
11. Okabe Y., Lecture Notes. Hokkaido Univ., 1985.
12. Okabe Y., A generalized fluctuation-dissipation theorem for one-dimensional diffusion process. Comm. Math. Phys. 98 (1985), 449-468.
13. Okabe Y., On KMO-Langevin equations for stationary Gaussian processes with T-positivity. J. Fac. Sci. Univ. Tokyo Sec. IA 33 (1986), 1-56.
14. Okabe Y., KMO-Langevin equation and fluctuation-dissipation theorem (I). Hokkaido Math. J. 15 (1986), 163-216.
15. Okabe Y., On long time tails of correlation functions for KMO-Langev in equations. Probability Theory and Mathematical Statistics, Lecture Notes in Math. 1229, Springer, Berlin, 1988, pp.391-397.
16. Okabe Y., On the theory of discrete KMO-Langevin equations with reflection positivity (II). Hokkaido Math. J. 17 (1988), 1-44.
17. Okabe Y. and Inoue A., On the exponential decay of the correlation functions for KMO-Langevin equations. Japan. J. Math. 18 (1992), 13-24.
18. Oobayashi K., Kohno T. and Utiyama H., Photon correlation spectroscopy of the non-Markovian Brownian motion of spherical particles. Phys. Rev. A 27 (1983), 2632-2641.
19. Pitman E.J.G., On the behaviour of the characteristic function of a probability distribution in the neighbourhood of the origin. J. Austral. Math. Soc. 8 (1968), 422-443.
20. Soni K. and Soni R.P., Slowly varying functions and asymptotic behaviour of a class of integral transforms II. J. Math. Anal. Appl. 49 (1975), 612-628.
21. Yaglom A.M., Correlation theory of stationary and related random functions 1,2. Springer, Berlin, 1987.