Lade, Steven J. Finite sampling interval effects in Kramers-Moyal analysis. (English) Zbl 1233.82033 Phys. Lett., A 373, No. 41, 3705-3709 (2009). Summary: Large sampling intervals can affect reconstruction of Kramers-Moyal coefficients from data. A new method, which is direct, non-stochastic and exact up to numerical accuracy, is developed to estimate these finite time effects. The method is applied numerically to biologically inspired examples. Exact finite time effects are also described analytically for two special cases. The approach developed will permit better evaluation of Langevin or Fokker-Planck based models from data with large sampling intervals. It can also be used to predict the sampling intervals for which finite time effects become significant. Cited in 4 Documents MSC: 82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics 37M10 Time series analysis of dynamical systems 82C70 Transport processes in time-dependent statistical mechanics 92C40 Biochemistry, molecular biology Keywords:Kramers-Moyal coefficients; Fokker-Planck equation; finite sampling interval; adjoint operator; molecular motors; tethered diffusion PDFBibTeX XMLCite \textit{S. J. Lade}, Phys. Lett., A 373, No. 41, 3705--3709 (2009; Zbl 1233.82033) Full Text: DOI arXiv References: [1] Friedrich, R.; Siegert, S.; Peinke, J.; Lück, S.; Siefert, M.; Lindemann, M.; Raethjen, J.; Deuschl, G.; Pfister, G., Phys. Lett. A, 271, 217 (2000) [2] Kriso, S.; Peinke, J.; Friedrich, R.; Wagner, P., Phys. Lett. A, 299, 2-3, 287 (2002) [3] Risken, H., The Fokker-Planck Equation: Methods of Solution and Applications (1984), Springer-Verlag: Springer-Verlag Berlin · Zbl 0546.60084 [4] Kuusela, T., Phys. Rev. E, 69, 3, 031916 (2004) [5] Friedrich, R.; Peinke, J.; Renner, C., Phys. Rev. Lett., 84, 22, 5224 (2000) [6] Ghasemi, F.; Sahimi, M.; Peinke, J.; Friedrich, R.; Jafari, G. R.; Tabar, M. R.R., Phys. Rev. E, 75, 6, 060102(R) (2007) [7] Friedrich, R.; Peinke, J., Phys. Rev. Lett., 78, 5, 863 (1997) [8] Renner, C.; Peinke, J.; Friedrich, R., J. Fluid Mech., 433, 383 (2001) [9] Gradišek, J.; Siegert, S.; Friedrich, R.; Grabec, I., Phys. Rev. E, 62, 3, 3146 (2000) [10] Sura, P.; Barsugli, J., Phys. Lett. A, 305, 5, 304 (2002) · Zbl 1001.82096 [11] Ragwitz, M.; Kantz, H., Phys. Rev. Lett., 87, 25, 254501 (2001) [12] Friedrich, R.; Renner, C.; Siefert, M.; Peinke, J., Phys. Rev. Lett., 89, 14, 149401 (2002) [13] Ragwitz, M.; Kantz, H., Phys. Rev. Lett., 89, 14, 149402 (2002) [14] Kleinhans, D.; Friedrich, R.; Nawroth, A.; Peinke, J., Phys. Lett. A, 346, 1-3, 42 (2005) [15] Kleinhans, D.; Friedrich, R., Phys. Lett. A, 368, 194 (2007) [16] Burgess, S.; Walker, M.; Wang, F.; Sellers, J. R.; White, H. D.; Knight, P. J.; Trinick, J., J. Cell Biol., 159, 6, 983 (2002) [17] Dunn, A. R.; Spudich, J. A., Nature Struct. Mol. Biol., 14, 246 (2007) [18] Shiroguchi, K.; Kinosita, K., Science, 316, 5828, 1208 (2007) [19] Vilfan, A., Biophys. J., 88, 6, 3792 (2005) [20] Zwanzig, R., Nonequilibrium Statistical Mechanics (2001), Oxford University Press: Oxford University Press New York · Zbl 1267.82001 [21] Gottschall, J.; Peinke, J., New J. Phys., 10, 8, 083034 (2008) [22] Raible, M.; Engel, A., Appl. Organometal. Chem., 18, 536 (2004) [23] S.J. Lade, Geometric and projection effects in Kramers-Moyal analysis, Phys. Rev. E, in press; S.J. Lade, Geometric and projection effects in Kramers-Moyal analysis, Phys. Rev. E, in press · Zbl 1233.82033 [24] Farahpour, F.; Eskandari, Z.; Bahraminasab, A.; Jafari, G.; Ghasemi, F.; Sahimi, M.; Reza Rahimi Tabar, M., Physica A, 385, 2, 601 (2007) [25] Kimiagar, S.; Jafari, G. R.; Tabar, M. R.R., J. Stat. Mech., 02010 (2008) [26] Jafari, G. R.; Fazeli, S. M.; Ghasemi, F.; Vaez Allaei, S. M.; Reza Rahimi Tabar, M.; Irajizad, A.; Kavei, G., Phys. Rev. Lett., 91, 22, 226101 (2003) [27] Kloeden, P. E.; Platen, E., Numerical Solution of Stochastic Differential Equations (1992), Springer-Verlag: Springer-Verlag Berlin · Zbl 0925.65261 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.