Document Zbl 0521.92008

Statistical properties of the asymmetric random telegraph signal, with applications to single-channel analysis. (English) Zbl 0521.92008

Math. Biosci. 64, 75-89 (1983).

Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0521.92008

MSC:

92Cxx	Physiological, cellular and medical topics
60G35	Signal detection and filtering (aspects of stochastic processes)
60K99	Special processes
94A40	Channel models (including quantum) in information and communication theory
91B99	Mathematical economics

Keywords:

asymmetric random telegraph signal; single-channel analysis; single-time- constant filter; modeling ionic channels; nerve membrane; distribution of number of jumps; density functions of pulse duration; autocorrelation; spectral density; Fokker-Planck equations; alternating Poisson process; Kolmogorov equations

Cite Review PDF

Full Text: DOI

References:

[1]	Abramowitz, M.; Stegun, I. A., Handbook of Mathematical Functions (1964), National Bureau of Standards: National Bureau of Standards Washington · Zbl 0515.33001
[2]	Bateman, H., Partial Differential Equations of Mathematical Physics (1944), Dover: Dover New York · Zbl 0063.00249
[3]	Bharucha-Reid, A. T., Elements of the Theory of Markov Processes and Their Applications (1960), McGraw-Hill: McGraw-Hill New York · Zbl 0095.32803
[4]	Colquhoun, D.; Hawkes, A. G., Relaxation and fluctuations of membrane currents that flow through drug-operated ion channels, Proc. Roy. Soc. London Ser. B, 199, 231-262 (1977)
[5]	Conti, F.; Wanke, E., Channel noise in nerve membranes and lipid bilayers, Quart Rev. Biophys., 8, 451-506 (1975)
[6]	Courant, R.; Hilbert, D., Methods of Mathematical Physics, Vol. II (1962), Interscience: Interscience New York · Zbl 0729.00007
[7]	Cox, D. R.; Miller, H. D., The Theory of Stochastic Processes (1965), Wiley: Wiley New York · Zbl 0149.12902
[8]	DeFelice, L. J., Introduction to Membrane Noise (1981), Plenum: Plenum New York
[9]	Ehrenstein, G.; Blumenthal, R.; Lattore, R.; Lecar, H., Kinetics of opening and closing of individual excitability-inducing material channels in a lipid bilayer, J. Gen. Physiol., 63, 707-721 (1974)
[11]	Jackson, M. B.; Lecar, H., Single postsynaptic channel currents in tissue cultured muscle, Nature, 282, 863-864 (1979)
[12]	Jones, D. S., Generalised Functions (1966), McGraw-Hill: McGraw-Hill New York · Zbl 0149.09403
[13]	Kenrick, G. W., The analysis of irregular motions with applications to the energy-frequency spectrum of static and of telegraph signals, Philos. Mag., 7, 176-196 (1929)
[14]	Lecar, H., Single-channel conductances and models of transport, (Adelman, W. J.; Goldman, D. E., The Biophysical Approach to Excitable Systems (1981), Plenum: Plenum New York), 109-121
[15]	Lecar, H.; Sachs, F., Membrane noise analysis, (Nelson, P. G.; Lieberman, M., Excitable Cells in Tissue Culture (1981), Plenum: Plenum New York), 137-172
[16]	Lighthill, M. J., Introduction to Fourier Analysis and Generalised Functions (1958), University Press: University Press Cambridge · Zbl 0078.11203
[17]	Machlup, S., Noise in semiconductors: spectrum of a two-parameter random signal, J. Appl. Phys., 25, 341-343 (1954) · Zbl 0055.20710
[18]	Parzen, E., Stochastic Processes (1962), Holden-Day: Holden-Day San Francisco · Zbl 0107.12301
[19]	Pawula, R. F., Generalizations and extensions of the Fokker-Planck-Kolmogorov equations, IEEE Trans. Inform. Theory, IT-13, 33-41 (1967) · Zbl 0154.42401
[20]	Pawula, R. F., The transition probability density function of the low-pass filtered random telegraph signal, Internat J. Control, 12, 25-32 (1970) · Zbl 0205.47501
[21]	Pawula, R. F., Statistical geometry of the smoothed random telegraph signal, Internat. J. Control, 16, 629-640 (1972) · Zbl 0246.94001
[22]	Pawula, R. F., The probability density and level-crossings of first-order non-linear systems driven by the random telegraph signal, Internat. J. Control, 25, 283-292 (1977)
[23]	Wax, N., Selected Papers on Noise and Stochastic Processes (1954), Dover: Dover New York · Zbl 0063.06485
[24]	Rickard, J. T., The zero-crossing interval statistics of the smoothed random telegraph signal, Inform Sci., 13, 253-268 (1977) · Zbl 0374.62006
[25]	Rickard, J. T.; Pawula, R. F., The zero crossing variance of the smoothed random telegraph signal, Internat. J. Control, 21, 743-752 (1975)
[27]	Verveen, A. A.; DeFelice, L. J., Membrane noise, Progr. Biophys. Molec. Biol., 28, 189-265 (1974)
[28]	Wax, N., Selected Papers on Noise and Stochastic Processes (1954), Dover: Dover New York · Zbl 0059.11903
[29]	Wonham, W. M., Transition probability densities of smoothed random telegraph signal, J. Electron. Control, 6, 376-384 (1959)
[30]	Wonham, W. M.; Fuller, A. T., Probability densities of the smoothed “random telegraph signal”, J. Electron. Control, 4, 567-576 (1958)

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.