The average conditional jumps for a white noise superposed on a linear trend are computed both theoretically and numerically and the contribution of the deterministic and random parts of the signal are given. The cases of infinite and finite time series are considered and the influence of the boundaries of the time series are determined. This is a simplified version of the problem of modeling noisy chaotic signals with a difference version of the Langevin equation using a statistical analysis of the conditional probabilities corresponding to the increasing and decreasing parts of the time series. Here we apply this method on individual monotone parts of the signal.
C. Vamos, M. Crăciun, Average conditional jump for a white noise superposed on a linear trend, 2007 International Conference on Engineering and Mathematics, Bilbao, July 9-11, 2007, pp. 51-56
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 Friedrich, R., Siegert, S., Peinke, J., Lick, St., Siefert, M., Lindemann, M., Rathjen, J., Deuschl, G., Pfister, G., Extracting model equations from experimental data, Phys, Lett, A, vol.271, 217-222, 2000.
 Gradisek, J., Siegert, S., Friedrich, R., Grabec, I., Analysis of time series from stochastic processes, Phys. Rev. E., vol. 62, 3146-3155, 2000
 Kusela, T, Sheperd, T., Hietarinta, J., A stochastic model for heart rate fluctuations, Phys. Rev. E. vol. 67, 061904, 2003.
 Siegert, S., Friedrich, R., Peinke, J., Analysis of data sets of stochastic systems, Phys. Lett. A. vol. 243, 275-280, 1998.
 Vamos, C., Automatic algorithm for monotone trend removal, Phys. Rev. E., vol. 75, 036705, 2007.