Abstract
Let {X(t),−∞<t<∞} be a continuous parameter, stationary, ergodic process. We consider random sampling times {τn} and show that for certain of these, if we can observe the bivariate process {τn,X(τn)} we are able to estimate consistently all finite-dimensional distributions of the process {X(t)}.
Research supported by N.S.F. Grant MCS 800 21 79.
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References
Blum, J.R. and Rosenblatt, Judah, On Random Sampling From A Stochastic Process, Ann. Math. Statist., 35, (1964), 1713–1717.
Doob, J.L., Stochastic Processes Depending On A Continuous Parameter, Trans. Am. Math. Soc., 42 (1937), 107–140.
Doob, J.L., Stochastic Processes, John Wiley, New York, 1953.
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© 1981 Springer-Verlag
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Blum, J.R., Boyles, R.A. (1981). Random sampling from a continuous parameter stochastic process. In: Dugué, D., Lukacs, E., Rohatgi, V.K. (eds) Analytical Methods in Probability Theory. Lecture Notes in Mathematics, vol 861. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097308
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DOI: https://doi.org/10.1007/BFb0097308
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