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The existence of smooth densities for the prediction filtering and smoothing problems |
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| Authors: | Robert J. Elliott Michael Kohlmann |
| Affiliation: | (1) Department of Mathematics, Auburn University, 36849, AL, U.S.A.;(2) Department of Mathematics, Rutgers University, 08903 New Brunswick, NJ, U.S.A.;(3) Courant Institute of Mathematical Sciences, New York University, 10012 New York, NY, U.S.A. |
| Abstract: | The qualitative behavior of buckled states of two different models of elastic beams is studied. It is assumed that random imperfections affect the governing nonlinear equations. It is shown that near the first critical value of the buckling load the stochastic bifurcation is described asymptotically by an algebraic equation whose coeffficients are Gaussian random variables. The corresponding asymptotic expansion for the displacement is to lowest order a Gaussian stochastic process.Work supported by NSF Grant No. DCR81-14726.Work supported by NSF Grant No. DMS87-01895. |
| Keywords: | 58F14 35C20 35F20 |
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