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Monrad, Ditlev Tsukahara, Hideatsu 2011-05-07T12:05:29Z 2011-05-07T12:05:29Z 10000-01-01 1996 We first consider convergence in law of measurable processes with a general parameter set and a state space. To this end, we need to investigate topological properties of the space of measurable functions which is the paths space of measurable processes. Also a characterization of compact sets in the space is derived and some functionals on the space are discussed. We then proceed to prove some properties of probability measures on the space of measurable functions. After investigating conditions on function spaces which guarantee that weak convergence may be proved by establishing finite-dimensional convergence and tightness, we prove necessary and sufficient conditions for convergence in law of measurable processes. These results are then applied to convergence of the prediction process; a special case where the given process is Markov is studied in detail. We also derive two results on the prediction process which is not in the field of weak convergence. One is on the asymptotic behavior of the prediction process under absolutely continuity, and the other is an example which shows that the prediction process may lost Markov property if one uses a larger filtration than the natural one. Made available in DSpace on 2011-05-07T12:05:29Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9712467.pdf: 3279184 bytes, checksum: 4afc4bc587b75307f0b2c41740d97218 (MD5) Previous issue date: 1996 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:36:31Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:14:44-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission ETDs are only available to UIUC Users without author permission U of I Only 9780591199499 AAI9712467 (UMI)AAI9712467 http://hdl.handle.net/2142/19372 eng Copyright 1996 Tsukahara, Hideatsu Mathematics Statistics Weak convergence and the prediction process text Statistics Statistics University of Illinois at Urbana-Champaign Dissertation Ph.D.