Abstract.
We propose a novel inverse method that utilizes a set of data to construct a simple equation that governs the stochastic process for which the data have been measured, hence enabling us to reconstruct the stochastic process. As an example, we analyze the stochasticity in the beat-to-beat fluctuations in the heart rates of healthy subjects as well as those with congestive heart failure. The inverse method provides a novel technique for distinguishing the two classes of subjects in terms of a drift and a diffusion coefficients which behave completely differently for the two classes of subjects, hence potentially providing a novel diagnostic tool for distinguishing healthy subjects from those with congestive heart failure, even at the early stages of the disease development.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. Torquato, Random Heterogeneous Materials (Springer, New York, 2002); C.L.Y. Yeong, S. Torquato, Phys. Rev. E 57, 495 (1998); C.L.Y. Yeong, S. Torquato, Phys. Rev. E 58, 224 (1998)
M. Sahimi, Heterogeneous Materials, Vol. II (Springer, New York, 2003)
R. Friedrich, J. Peinke, Phys. Rev. Lett. 78, 863 (1997)
R. Friedrich, J. Peinke, C. Renner, Phys. Rev. Lett. 84, 5224 (2000)
R. Friedrich, Th. Galla, A. Naert, J. Peinke, Th. Schimmel, in A Perspective Look at Nonlinear Media, edited by J. Parisi, S.C. Muller, W. Zimmermann (Springer, Berlin, 1997), p. 313; R. Friedrich, et al., Phys. Lett. A 271, 217 (2000)
M. Siefert, A. Kittel, R. Friedrich, J. Peinke, Eur. Phys. Lett. 61, 466 (2003); S. Kriso, et al., Phys. Lett. A 299, 287 (2002); S. Siegert, R. Friedrich, J. Peinke, Phys. Lett. A 243, 275 (1998)
H. Risken, The Fokker-Planck Equation (Springer, Berlin, 1984)
G.R. Jafari, S.M. Fazlei, F. Ghasemi, S.M. Vaez Allaei, M.R. Rahimi Tabar, A. Iraji Zad, G. Kavei, Phys. Rev. Lett. 91, 226101 (2003)
C. Renner, J. Peinke, R. Friedrich, J. Fluid Mech. 433, 383 (2001)
M. Ragwitz, H. Kantz, Phys. Rev. Lett. 87, 254501 (2001)
R. Friedrich, C. Renner, M. Siefert, J. Peinke, Phys. Rev. Lett. 89, 149401 (2002)
J. Davoudi, M.R. Rahimi Tabar, Phys. Rev. Lett. 82, 1680 (1999)
C.-K. Peng, J. Mietus, J.M. Hausdorff, S. Havlin, H.E. Stanley, A.L. Goldberger, Phys. Rev. Lett. 70, 1343 (1993)
A. Bunde, S. Havlin, J.W. Kantelhardt, T. Penzel, J.-H. Peter, K. Voigt, Phys. Rev. Lett. 85, 3736 (2000)
P. Bernaola-Galvan, P.Ch. Ivanov, L.N. Amaral, H.E. Stanley, Phys. Rev. Lett. 87, 168105 (2001)
V. Schulte-Frohlinde, Y. Ashkenanzy, P.Ch. Ivanov, L. Glass, A.L. Goldberger, H.E. Stanley, Phys. Rev. Lett. 87, 068104 (2001)
Y. Ashkenazy, P.Ch. Ivanov, Shlomo Havlin, C.-K. Peng, A.L. Goldberger, H.E. Stanley, Phys. Rev. Lett. 86, 1900 (2001)
T. Kuusela, Phys. Rev. E 69, 031916 (2004)
M.M. Wolf, G.A. Varigos, D. Hunt, J.G. Sloman, Med. J. Aust. 2, 52 (1978)
P.Ch. Ivanov, A. Bunde, L.A.N. Amaral, S. Havlin, J. Fritsch-Yelle, R.M. Baevsky, H.E. Stanley, A.L. Goldberger, Europhys. Lett. 48, 594 (1999)
P.Ch. Ivanov, L.A.N. Amaral, A.L. Goldberger, S. Havlin, M.G. Rosenblum, Z. Struzik, H.E. Stanley, Nature (London) 399, 461 (1999)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ghasemi, F., Peinke, J., Sahimi, M. et al. Regeneration of stochastic processes: an inverse method . Eur. Phys. J. B 47, 411–415 (2005). https://doi.org/10.1140/epjb/e2005-00339-4
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2005-00339-4