Aihara, Shin-Ichi; Bagchi, Arunabha Infinite dimensional parameter identification for stochastic parabolic systems. (English) Zbl 0681.93063 Stat. Probab. Lett. 8, No. 3, 279-287 (1989). Summary: The infinite dimensional parameter estimation for stochastic heat diffusion equations is considered using the method of sieves [see U. Grenander, “Abstract inference” (1981; Zbl 0505.62069 )]. The consistency property is also studied for the long run data. Cited in 6 Documents MSC: 93E10 Estimation and detection in stochastic control theory 93C20 Control/observation systems governed by partial differential equations 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 35R60 PDEs with randomness, stochastic partial differential equations 80A20 Heat and mass transfer, heat flow (MSC2010) 93E12 Identification in stochastic control theory Keywords:inference for stochastic process; stochastic heat diffusion equations; method of sieves Citations:Zbl 0505.62069 PDFBibTeX XMLCite \textit{S.-I. Aihara} and \textit{A. Bagchi}, Stat. Probab. Lett. 8, No. 3, 279--287 (1989; Zbl 0681.93063) Full Text: DOI References: [1] Adams, R. A., Sobolev Spaces (1975), Academic Press: Academic Press New York · Zbl 0186.19101 [2] Aihara, S. I.; Sunahara, Y., Identification of an infinite dimensional parameter for stochastic diffusion equations, SIAM J. Control Optim., 26, 1062-1075 (1988) · Zbl 0667.93061 [3] Bagchi, A., Identification for a hereditary system with distributed delay, System Control Lett., 5, 339-345 (1985) · Zbl 0568.93064 [4] Bagchi, A.; Borkar, V., Parameter identification on infinite dimensional linear systems, Stochastics, 12, 201-213 (1984) · Zbl 0541.93072 [5] Balakrishnan, Identification and stochastic control of a class of distributed parameter systems with boundary noise, (Lecture Notes in Econom. Math. Systems, 107 (1975), Springer: Springer New York) · Zbl 0318.93033 [6] Bensoussan, A., Filtrage Optimal des System Lineaires (1971), Dunod: Dunod Paris [7] Curtain, R. F.; Kotelenez, P., Stochastic model for uncertain flexible systems, Automatica, 23, 657-661 (1987) · Zbl 0631.93069 [8] Grenander, U., Abstract Inference (1981), Wiley: Wiley New York · Zbl 0673.62088 [9] Lions, J. L., Quelques Methodes de Resolution des Problemes aux Limites Non Lineaires (1969), Dunod: Dunod Paris · Zbl 0189.40603 [10] Lions, J. L.; Magenes, E., (Non-Homogeneous Boundary Value Problems and Applications, 1 (1972), Springer: Springer Berlin) · Zbl 0223.35039 [11] Mizohata, S., The Theory of Partial Differential Equations (1973), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0263.35001 [12] Nguyen, H.; Pham, T. D., Identification of nonstationary model by the method of sieves, SIAM J. Control Optim., 20, 603-611 (1982) · Zbl 0488.62062 [13] Paradoux, E., Equations aux derivees partielles stochastiques non lineaireş monotones, (Thesis (1975), Université Paris XI: Université Paris XI Paris) [14] Tanabe, H., Equations of Evolutions (1979), Pitman: Pitman London [15] Wong, E., Stochastic Processes in Information and Dynamical Systems (1971), McGraw-Hill: McGraw-Hill New York · Zbl 0245.60001 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.