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Applying the EKF to stochastic differential equations with level effects. (English) Zbl 0982.93070

The authors consider a nonlinear filtering problem for a model with multiplicative noise. For a restricted class of systems of stochastic differential equations, they propose a transformation such that the transformed system is a system with additive noise.

MSC:

93E11 Filtering in stochastic control theory
93C10 Nonlinear systems in control theory
93B17 Transformations
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[1] Aı̈t-Sahalia, Y. (1999). Maximum likelihood estimation of discretely sampled diffusions: A closed-form approach. Working paper. Department of Economics, Princeton University.
[2] Baadsgaard, M. T. (1996). Estimation in stochastic differential equations. Master’s thesis, Department of Mathematical Modelling. Lyngby, Denmark.
[3] Baadsgaard, M., Nielsen, J. N., Spliid, H., Madsen, H., & Preisel, M. (1997). Estimation in stochastic differential equations with a state dependent diffusion term. In Y. Sawaragi & S. Sagara (Eds.), SYSID ’97 — 11th IFAC symposium on system identification, IFAC.
[4] Black, F.; Scholes, M., The pricing of options and corporate liabilities, Journal of political economy, 81, 637-654, (1973) · Zbl 1092.91524
[5] Bohlin, T.; Graebe, S.F., Issues in nonlinear stochastic grey-box identification, International journal of adaptive control and signal processing, 9, 6, 465-490, (1995)
[6] Chan, K.C.; Karolyi, G.A.; Longstaff, F.A.; Sanders, A.B., An empirical comparison of alternative models of the short-term interest rate, Journal of finance, 47, 1209-1227, (1992)
[7] Feller, W., Two singular diffusion problems, Annals of mathematics, 54, 1, 173-182, (1951) · Zbl 0045.04901
[8] Graebe, S. F. (1990a). IDKIT: A software gray box identification: Mathematical reference. Technical Report, TRITA-REG 90/03, Automatic Control, Royal Institute of Technology, Stockholm, Sweden.
[9] Graebe, S. F. (1990b). IDKIT: A software guide for gray box identification, user’s guide, version RT-1.0. Technical Report, TRITA-REG 90/04, Automatic Control, Royal Institute of Technology, Stockholm, Sweden.
[10] Jazwinski, A.H., Stochastic processes and filtering theory, (1970), Academic Press New York · Zbl 0203.50101
[11] Kloeden, P.E.; Platen, E., Numerical solutions of stochastic differential equations, (1995), Springer Heidelberg · Zbl 0858.65148
[12] Madsen, H. (1985). Statistically determined dynamical models for climate processes. Ph.D. Thesis, IMSOR, DTH, Lyngby.
[13] Madsen, H., & Melgaard, H. (1991). The mathematical and numerical methods used in CTLSM — a program for ML-estimation in stochastic, continuous time dynamical models. Technical Report, Institute of Mathematical Statistics and Operations Research.
[14] Maybeck, P.S., Stochastic models, estimation and control, (1982), Academic Press London · Zbl 0546.93063
[15] Melgaard, H., & Madsen, H. (1993). CTLSM version 2.6 — a program for parameter estimation in stochastic differential equations. Technical Report, IMSOR. No. 1.
[16] Mortensen, R.E., Mathematical problems of modeling stochastic nonlinear dynamic systems, Journal of statistical physics, 1, 271-296, (1969)
[17] Nielsen, J. N., Madsen, H., & Melgaard, H. (2000a). Estimating parameters in discretely, partially observed stochastic differential equations. Technical Report 2000-7, Department of Mathematical Modelling, Technical University of Denmark, Lyngby, Denmark.
[18] Nielsen, J.N.; Vestergaard, M.; Madsen, H., Estimation in continuous-time stochastic volatility models using nonlinear filters, International journal of theoretical and applied finance, 3, 2, 279-308, (2000) · Zbl 1154.91467
[19] Øksendal, B., Stochastic differential equations, (1995), Springer Heidelberg
[20] Wang, C. (1994). Stochastic differential equations and a biological system. Ph.D. Thesis, Institute of Mathematical Modelling, The Technical University of Denmark. Lyngby, Denmark.
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