Abstract
The barrier problem consisting in estimating the probability (1) is solved when the process u(z) belongs to a class of sine series with independent coefficients. The solution is obtained by identifying the process u with the positions of a vibrating string forced by white noise, for which the same barrier problem has been solved in a previous paper ([2]).
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References
Cabaña, E.M.: The vibrating string forced by white noise. Z. Wahrscheinlichkeitstheorie verw. Geb. 15, 111–130 (1970).
Cabaña, E.M.: On barrier problems for the vibrating string. Z. Wahrscheinlichkeitstheorie verw. Geb. 22, 13–24 (1972).
Kahane, J.P.: Some random series of functions. Heath Mathematical Monographs. Lexington, Mass.: Heath 1968.
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Cabaña, E.M. On the barrier problem for sine series with independent Gaussian coefficients. Z. Wahrscheinlichkeitstheorie verw Gebiete 24, 215–219 (1972). https://doi.org/10.1007/BF00532533
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DOI: https://doi.org/10.1007/BF00532533