Lim, S. C.; Teo, L. P. The fractional oscillator process with two indices. (English) Zbl 1156.82010 J. Phys. A, Math. Theor. 42, No. 6, Article ID 065208, 34 p. (2009). Summary: We introduce a new fractional oscillator process which can be obtained as a solution of a stochastic differential equation with two fractional orders. Basic properties such as fractal dimension and short-range dependence of the process are studied by considering the asymptotic properties of its covariance function. By considering the fractional oscillator process as the velocity of a diffusion process, we derive the corresponding diffusion constant, fluctuation-dissipation relation and mean-square displacement. The fractional oscillator process can also be regarded as a one-dimensional fractional Euclidean Klein-Gordon field, which can be obtained by applying the Parisi-Wu stochastic quantization method to a nonlocal Euclidean action. The Casimir energy associated with the fractional field at positive temperature is calculated by using the zeta function regularization technique. Cited in 34 Documents MSC: 82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics PDFBibTeX XMLCite \textit{S. C. Lim} and \textit{L. P. Teo}, J. Phys. A, Math. Theor. 42, No. 6, Article ID 065208, 34 p. (2009; Zbl 1156.82010) Full Text: DOI arXiv