Maximum cross section method in the filtering problem for continuous systems with Markovian switching

References

[1] T. A. Averina, A randomized maximum cross-section method to simulate random structure systems with distributed transitions. Numer. Anal. Appl. 9 (2016), No. 3, 179–190.10.1134/S1995423916030010Suche in Google Scholar

[2] T. A. Averina, Statistical Modelling of Solutions to Stochastic Differential Equations and Systems with Random Structure. Siberian Branch of RAS, Novosibirsk, 2019 (in Russian).Suche in Google Scholar

[3] T. A. Averina and K. A. Rybakov, Maximum cross section method in optimal filtering of jump-diffusion random processes. In: Proc. 15th Int. Asian School-Seminar on Optimization Problems of Complex Systems. IEEE, 2019, pp. 8–11.10.1109/OPCS.2019.8880234Suche in Google Scholar

[4] T. A. Averina and K. A. Rybakov, Using maximum cross section method for filtering jump-diffusion random processes. Russ. J. Numer. Anal. Math. Modelling 35 (2020), No. 2, 55–67.10.1515/rnam-2020-0005Suche in Google Scholar

[5] A. Bain and D. Crisan, Fundamentals of Stochastic Filtering. Springer, 2009.10.1007/978-0-387-76896-0Suche in Google Scholar

[6] Y. Bao, C. Chiarella, and B. Kang, Particle filters for Markov-switching stochastic volatility models. In: The Oxford Handbook of Computational Economics and Finance (Eds. S.-H. Chen, M. Kaboudan, and Y.-R. Du). Oxford University Press, 2018, pp. 249–266.10.1093/oxfordhb/9780199844371.013.9Suche in Google Scholar

[7] V. A. Boldinov, V. A. Bukhalev, S. P. Pryadkin, and A. A. Skrynnikov, Control of the probability distribution of a system state based on its structure indicator. J. Comput. Syst. Sci. Int. 55 (2016), No. 3, 333–340.10.1134/S1064230716020039Suche in Google Scholar

[8] N. V. Chernykh and P. V. Pakshin, Numerical solution algorithms for stochastic differential systems with switching diffusion. Autom. Remote Control 74 (2013), No. 12, 2037–2063.10.1134/S0005117913120072Suche in Google Scholar

[9] J. Chevallier and S. Goutte, On the estimation of regime-switching Lévy models. Stud. Nonlinear Dyn. E. 21 (2017), No. 1, 3–29.10.1515/snde-2016-0048Suche in Google Scholar

[10] K. Chugai, I. Kosachev, and K. Rybakov, Approximate MMSE and MAP estimation using continuous-time particle filter. AIP Conf. Proc. 2181 (2019), 020001.10.1063/1.5135661Suche in Google Scholar

[11] K. N. Chugai, I. M. Kosachev, and K. A. Rybakov, Approximate filtering methods in continuous-time stochastic systems. In: Smart Innovation, Systems and Technologies, Vol. 173. Springer, 2020, pp. 351–371.10.1007/978-981-15-2600-8_24Suche in Google Scholar

[12] M. Ghosh, A. Arapostathis, and S. Marcus, Optimal control of switching diffusions with application to flexible manufacturing systems. SIAM J. Control Optim. 31 (1993), No. 5, 1183–1204.10.21236/ADA454850Suche in Google Scholar

[13] F. Karamé, A new particle filtering approach to estimate stochastic volatility models with Markov-switching. Econ. Stat. 8 (2018), No. C, 204–230.10.1016/j.ecosta.2018.05.004Suche in Google Scholar

[14] I. E. Kazakov and V. M. Artem’ev, Optimization of Dynamic Systems of Random Structure. Nauka, Moscow, 1980 (in Russian).Suche in Google Scholar

[15] C. Kumar and T. Kumar, On explicit tamed Milstein-type scheme for stochastic differential equation with Markovian switching. J. Comput. Appl. Math. 377 (2020), 112917.10.1016/j.cam.2020.112917Suche in Google Scholar

[16] X. R. Li and V. P. Jilkov, Survey of maneuvering target tracking. Part V: Multiple-model methods. IEEE Trans. Aerospace Electronic Syst. 41 (2005), No. 4, 1255–1321.10.1109/TAES.2005.1561886Suche in Google Scholar

[17] T. Lux, Inference for nonlinear state space models: A comparison of different methods applied to Markov-switching multi-fractal models. Econ. Stat. 10 (2020).10.1016/j.ecosta.2020.03.001Suche in Google Scholar

[18] G. A. Mikhailov and T. A. Averina, The maximal section algorithm in the Monte Carlo method. Doklady Math. 80 (2009), No. 2, 671–673.10.1134/S1064562409050111Suche in Google Scholar

[19] G. A. Mikhailov and A. V. Voitishek, Numerical Statistical Modelling. Monte Carlo Methods. Publ. House Akademia, Moscow, 2006 (in Russian).Suche in Google Scholar

[20] S. L. Nguyen, T. A. Hoang, D. T. Nguyen, and G. Yin, Milstein-type procedures for numerical solutions of stochastic differential equations with Markovian switching. SIAM J. Numer. Anal. 55 (2017), No. 2, 953–979.10.1137/16M1084730Suche in Google Scholar

[21] E. A. Rudenko, Finite-dimensional recurrent algorithms for optimal nonlinear logical-dynamical filtering. J. Comput. Syst. Sci. Int. 55 (2016), No. 1, 36–58.10.1134/S1064230715060131Suche in Google Scholar

[22] O. A. Stepanov and A. S. Nosov, A map-aided navigation algorithm without preprocessing of field measurements. Gyroscopy Navig. 11 (2020), No. 2, 162–175.10.1134/S207510872002008XSuche in Google Scholar

[23] O. A. Stepanov, V. A. Vasiliev, A. B. Toropov, A. V. Loparev, and M. V. Basin, Efficiency analysis of a filtering algorithm for discrete-time linear stochastic systems with polynomial measurements. J. Franklin Inst. 356 (2019), No. 10, 5573–5591.10.1016/j.jfranklin.2019.02.036Suche in Google Scholar

[24] A. P. Trifonov and Yu. S. Shinakov, Joint Discrimination of Signals and Estimation of Their Parameters against the Background of Interferences. Radio i Svyaz, Moscow, 1986 (in Russian).Suche in Google Scholar

[25] V. A. Tupysev and Yu. A. Litvinenko, Application of polynomial-type filters to integrated navigation systems with modular architecture. In: Proc. 26th Int. Conf. on Integrated Navigation Systems. IEEE, 2019, pp. 1–4.10.23919/ICINS.2019.8769422Suche in Google Scholar

[26] M. S. Yarlykov and S. M. Yarlykova, Optimal algorithms of complex nonlinear processing of vector discrete-continuous signals. Radiotekhnika (2004), No. 7, 18–29 (in Russian).Suche in Google Scholar