Aihara, Shin Ichi; Sunahara, Yoshifumi; Ishikawa, Masaaki Filtering for systems modelled by variational inequalities associated with the one phase stochastic Stefan problem. (English) Zbl 0642.93058 Int. J. Control 47, No. 1, 1-15 (1988). According to the abstract: “The one phase stochastic Stefan problem with random disturbance is expressed by using the stochastic variational inequality. The key idea in studying the existence and uniqueness properties of the solution of a stochastic variational inequality is the introduction of the theory of non-linear stochastic differential equations. The filering equation under noisy observations is derived by applying the martingale representation technique. By using the finite difference approximation method, the derived non-linear filter equation is realized numerically and compared with simulation results.” Reviewer: C.Wang MSC: 93E11 Filtering in stochastic control theory 49J40 Variational inequalities 93C10 Nonlinear systems in control theory 35R35 Free boundary problems for PDEs 60G99 Stochastic processes 93E25 Computational methods in stochastic control (MSC2010) Keywords:one phase stochastic Stefan problem; stochastic variational inequality; filering equation; noisy observations; martingale representation; finite difference approximation PDFBibTeX XMLCite \textit{S. I. Aihara} et al., Int. J. Control 47, No. 1, 1--15 (1988; Zbl 0642.93058) Full Text: DOI References: [1] BENSOUSSAN A., Filtrage Optimal des Systèmes Linéaires (1971) · Zbl 0231.93022 [2] FUJISAKI M., Osaka J. Math. 9 pp 19– (1972) [3] DOI: 10.1512/iumj.1975.24.24086 · Zbl 0334.49002 · doi:10.1512/iumj.1975.24.24086 [4] DOI: 10.1080/00207178708933709 · Zbl 0615.93065 · doi:10.1080/00207178708933709 [5] KINDERLEHRER D., An Introduction to Variational Inequality and their Applications (1980) · Zbl 0457.35001 [6] LIONS J. L., Quelques Méthodes de Rèsolution des Problemes aux Limites Non Linéaires (1969) [7] PARDOUX E., Stochastics 3 pp 127– (1979) · Zbl 0424.60067 · doi:10.1080/17442507908833142 [8] DOI: 10.1016/0005-1098(75)90026-6 · doi:10.1016/0005-1098(75)90026-6 [9] SUNAHARA , Y. , AIHARA , S. I. , and ISHIKAWA , M. , 1982 ,Proc. of 3rd Symp. on Control of Distributed Parameter Systems, Toulouse ( Oxford : Pergamon Press ) p. 291 . [10] DOI: 10.1016/0020-7225(65)90045-5 · Zbl 0131.16401 · doi:10.1016/0020-7225(65)90045-5 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.