[78] E. Kalnay. Atmospheric Modelling, Data Assimilation and Predictability. Cambridge University Press (2003).

[79] I. Karatzas and S.E. Shreve. Brownian Motion and Stochastic Calculus. Springer (1996).

[80] T. Karvonen, S. Bonnabel, E. Moulines and S. Särkkä. On stability of a class of filters for non-linear stochastic systems. arXiv e-print, arXiv:1809.05667 (2018).

[81] D. Kelly, K.H.J. Law, and A.M. Stuart. Well-posedness and accuracy of the ensemble Kalman filter in discrete and continuous time. Nonlinearity. vol. 27, no. 10. pp. 2579-2603 (2014).

[82] D. Kelly, A.J. Majda, and X.T. Tong. Concrete ensemble Kalman filters with rigorous catastrophic filter divergence. Proceedings of the National Academy of Sciences of the United States of America. vol 112, no. 34. pp. 10589-10594 (2015).

[83] G. Kitagawa. A Monte Carlo Filtering and Smoothing Method for Non-Gaussian Nonlinear State Space Models. Proceedings of the 2nd U.S.-Japan Joint Seminar on Statistical Time Series Analysis: pp. 110-131 (1993).

[84] G. Kitagawa. Monte Carlo filter and smoother for non-Gaussian nonlinear state space models. Journal of Computational and Graphical Statistics. vol. 5, no.1, pp 1-25 (1996).

[85] M. Kohlmann and S. Tang. Multidimensional backward stochastic Riccati equations and applications. SIAM Journal on Control Optimization. vol. 41, no. 6. pp. 1696-1721 (2003).

[86] G.M. Krause. Bounds for the Variation of Matrix Eigenvalues and Polynomial Roots. Linear Algebra and its Applications. vol. 208-209. pp. 73-82 (1994).

[87] V. Kucera. A Contribution to Matrix Quadratic Equations. IEEE Transactions on Automatic Control. vol. 17, no. 3. pp. 344-347 (1972).

[88] H. Kunita. Asymptotic behavior of the nonlinear filtering errors of Markov processes. Journal of Multivariate Analysis. vol. 1, no. 4. pp. 365-393 (1971).

[89] H. Kwakernaak and R. Sivan. Linear Optimal Control Systems. Wiley-Interscience (1972).

[90] E. Kwiatkowski and J. Mandel. Convergence of the Square Root Ensemble Kalman Filter in the Large Ensemble Limit. SIAM/ASA Journal on Uncertainty Quantification. vol. 3, no. 1. pp. 1-17 (2015).

[91] P. Lancaster and L. Rodman. Algebraic Riccati Equations. Oxford University Press (1995).

[92] T. Lange. Derivation of ensemble Kalman-Bucy filters with unbounded nonlinear coefficients. Nonlinearity. vol. 35, no. 2. (2021).

[93] T. Lange and W. Stannat. Mean field limit of Ensemble Square Root Filters-discrete and continuous time. Foundations of Data Science. vol. 3, no. 3. pp. 563-588 (2021).

[94] T. Lange and W. Stannat. On the continuous time limit of the ensemble Kalman filter. Mathematics of Computation. vol. 90, no. 327. pp. 233-265 (2021).

[95] T. Lange and W. Stannat. On the continuous time limit of ensemble square root filters. Communications in Mathematical Sciences. vol. 19, no. 7. (2021).

[96] B.F. La Scala, R.R. Bitmead, and M.R. James. Conditions for stability of the extended Kalman filter and their application to the frequency tracking problem. Mathematics of Control, Signals and Systems. vol. 8, no. 1. (1995).
[97] K.J.H. Law, A.M. Stuart and K. Zygalakis. Data Assimilation: A Mathematical Introduction. Springer (2015).

[98] K.J.H. Law, H. Tembine and R. Tempone. Deterministic Mean-Field Ensemble Kalman Filtering. SIAM Journal on Scientific Computing. vol. 38, no. 3. pp. A1251-A1279 (2016).

[99] F. Le Gland, V. Monbet and V.D. Tran. Large sample asymptotics for the ensemble Kalman filter. Chapter 22 in The Oxford Handbook of Nonlinear Filtering. pp. 598-631 (2011).

[100] H. Lee, and Y. Lim. Invariant metrics, contractions and nonlinear matrix equations. Nonlinearity. vol. 21, no. 4. pp. 857 (2008).

[101] B.C. Levy, and M. Zorzi. A contraction analysis of the convergence of risk-sensitive filters. SIAM Journal on Control and Optimization. vol. 54, no. 4. pp. 2154-2173 (2016).

[102] K.A. Lisaeter, J. Rosanova and G. Evensen. Assimilation of ice concentration in a coupled ice-ocean model using the Ensemble Kalman Filter. Ocean Dynamics. vol. 53, no. 4. pp. 368-388 (2003).

[103] D.M. Livings, S.L. Dance and N.K. Nichols. Unbiased Ensemble Square Root Filters. Physica D: Nonlinear Phenomena. vol. 237, no. 8. pp. 1021-1028 (2008).

[104] A.J. Majda and J. Harlim. Filtering Complex Turbulent Systems. Cambridge University Press (2012).

[105] A.J. Majda and X.T. Tong. Performance of Ensemble Kalman Filters in Large Dimensions. Communications in Mathematical Sciences. vol. 71, no. 5. pp. 892-937 (2018).

[106] J. Mandel, L. Cobb, and J.D. Beezley. On the convergence of the ensemble Kalman filter. Applications of Mathematics. vol. 56, no. 6. pp. 533-541 (2011).

[107] H.P. McKean. A class of Markov processes associated with nonlinear parabolic equations. Proceedings of the National Academy of Sciences. vol. 56, no. 6. pp.1907-1911 (1966).

[108] H.L. Mitchell, P.L. Houtekamer and G. Pellerin. Ensemble size, balance, and model-error representation in an ensemble Kalman filter. Monthly Weather Review. vol. 130, no. 11. pp. 2791-2808 (2002).

[109] B.P. Molinari. The time-invariant linear-quadratic optimal control problem. Automatica. vol. 13, no. 4. pp. 347-357 (1977).

[110] G. Naevdal, L.M. Johnsen, S.I. Aanonsen and E.H. Vefring. Reservoir monitoring and continuous model updating using ensemble Kalman filter. In Proceedings of the 2003 SPE Annual Technical Conference and Exhibition, Denver, Colorado (October, 2003).

[111] D. Ocone and E. Pardoux. Asymptotic stability of the optimal filter with respect to its initial condition. SIAM Journal on Control and Optimization. vol. 34, no. 1. pp. 226-243 (1996).

[112] E. Ott, B.R. Hunt, I. Szunyogh, A.V. Zimin, E.J. Kostelich, M. Corazza, E. Kalnay, D. Patil, and J.A. Yorke. A local ensemble Kalman filter for atmospheric data assimilation. Tellus A. vol. 56, no. 5. pp. 415-428 (2004).

[113] N. Oudjane and S. Rubenthaler. Stability and uniform particle approximation of nonlinear filters in case of non ergodic signals. Stochastic Analysis and Applications. vol. 23, no. 3. 421-448 (2005).
[114] N. Papadakis, E Mémin, A Cuzol, and N Gengembre. Data assimilation with the weighted ensemble Kalman filter. Tellus A: Dynamic Meteorology and Oceanography. vol. 62, no. 5. pp. 673–697 (2010).

[115] P. Park and T. Kailath. Convergence of the DRE solution to the ARE strong solution. IEEE Transactions on Automatic Control. vol. 42, no. 4. 573–578 (1997).

[116] S. Pathiraja, S. Reich, and W. Stannat. McKean-Vlasov SDEs in nonlinear filtering. SIAM Journal on Control and Optimization. vol. 59, no. 6. pp. 4188–4215 (2021).

[117] M-A. Poubelle, I.R. Petersen, M.R. Gevers, and R.R. Bitmead. A Miscellany of Results on an Equation of Count J. F. Riccati. IEEE Transactions on Automatic Control. vol. 31, no. 7. pp. 651–654 (1986).

[118] P. Rebeschini and R. Van Handel. Can local particle filters beat the curse of dimensionality? The Annals of Applied Probability. vol. 25, no. 5. pp. 2809–2866 (2015).

[119] S. Reich. Data assimilation: A dynamic homotopy-based coupling approach. arXiv e-print, arXiv:2209.05279 (2022).

[120] S. Reich and C.J. Cotter. Ensemble filter techniques for intermittent data assimilation. Large Scale Inverse Problems: Computational Methods and Applications in the Earth Sciences (eds: M. Cullen, M.A. Freitag, S. Kindermann, R. Scheichl), pages 91–134. De Gruyter Publishers (2013). See also: arXiv e-print, arXiv:1208.6572 (2012).

[121] S. Reich and C.J. Cotter. Probabilistic Forecasting and Bayesian Data Assimilation. Cambridge University Press (2015).

[122] S. Reich and S. Shin. On the consistency of ensemble transform filter formulations. Journal of Computational Dynamics. vol. 1, no. 1. pp. 177–189 (2014).

[123] K. Reif, S. Gunther, E. Yaz, and R. Unbehauen. Stochastic stability of the continuous-time extended Kalman filter. IEE Proceedings – Control Theory and Applications. vol. 147, no. 1. pp. 45–52 (2000).

[124] H. Ruzayqat, N.K. Chada, and A. Jasra. Multilevel estimation of normalization constants using ensemble Kalman-Bucy filters. Statistics and Computing. vol. 32, no. 3. pp. 1–25 (2022).

[125] P. Sakov and P.R. Oke. A deterministic formulation of the ensemble Kalman filter: an alternative to ensemble square root filters. Tellus A. vol. 60, no. 2. pp. 361–371 (2008).

[126] P. Sakov and P.R. Oke. Implications of the Form of the Ensemble Transformation in the Ensemble Square Root Filters. Monthly Weather Review. vol. 136, no. 3. pp. 1042–1053 (2008).

[127] C. Schillings and A.M. Stuart. Convergence analysis of ensemble Kalman inversion: the linear, noisy case. Applicable Analysis. vol. 97, no. 1. pp. 107–123 (2017).

[128] C. Schillings and A.M. Stuart. Analysis of the ensemble Kalman filter for inverse problems. SIAM Journal on Numerical Analysis. vol. 55, no. 3. pp. 1264–1290 (2017).

[129] A. Seiler, G. Evensen, J.-A. Skjervheim, J. Hove, and J.G. Vab. Using the EnKF for history matching and uncertainty quantification of complex reservoir models. In Large-Scale Inverse Problems and Quantification of Uncertainty (eds: L. Biegler, G. Biros, O. Ghattas, M. Heinkenschloss, D. Keyes, B. Mallick, Y. Marzouk, L. Tenorio, B. van Bloemen Waanders and K. Willcox). pp. 247–271. John Wiley & Sons, New York (2010).
[130] B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla, M.I. Jordan and S.S. Sastry. Kalman Filtering with Intermittent Observations. IEEE Transactions on Automatic Control. vol. 49, no. 9. pp. 1453-1464 (2004).

[131] T. Ström. On logarithmic norms. SIAM Journal on Numerical Analysis. vol. 12, no. 5. pp. 741-753 (1975).

[132] A. Taghvaei and P.G. Mehta. An optimal transport formulation of the linear feedback particle filter. In Proc. of the 2016 American Control Conference (ACC), Boston, USA (July, 2016).

[133] A. Taghvaei and P.G. Mehta. A Survey of Feedback Particle Filter and related Controlled Interacting Particle Systems (CIPS). arXiv e-print, arXiv:2301.00935 (2023).

[134] A. Taghvaei, P.G. Mehta, and S.P. Meyn. Diffusion map-based algorithm for gain function approximation in the feedback particle filter. SIAM/ASA Journal on Uncertainty Quantification. vol. 8, no. 3. pp. 1090-1117 (2020).

[135] A. Tanwani and O. Yufereva. Error covariance bounds for suboptimal filters with Lipschitzian drift and Poisson-sampled measurements. Automatica. vol. 122. (2020).

[136] M.K. Tippett, J.L. Anderson, C.H. Bishop, T.M. Hamill, and J.S. Whitaker. Ensemble square root filters. Monthly Weather Review. vol. 131, no. 7. pp. 1485-1490 (2003).

[137] X.T. Tong, A.J. Majda, and D. Kelly. Nonlinear stability and ergodicity of ensemble based Kalman filters. Nonlinearity. vol. 29, no. 2. pp 657-691 (2016).

[138] X.T. Tong, A.J. Majda, and D. Kelly. Nonlinear stability of the ensemble Kalman filter with adaptive covariance inflation. Communications in Mathematical Sciences. vol. 14, no. 5. pp. 1283-1313 (2016).

[139] R. Van Handel. Observability and nonlinear filtering. Probability Theory and Related Fields. vol. 145, no. 1-2. pp. 35-74 (2009).

[140] R. Van Handel. The stability of conditional Markov processes and Markov chains in random environments. The Annals of Probability. vol. 37, no. 5. 1876-1925 (2009).

[141] R. Van Handel. Uniform time average consistency of Monte Carlo particle filters. Stochastic Processes and their Applications. vol. 119, no. 11. pp. 3835-3861 (2009).

[142] J.S. Whitaker and T.M. Hamill. Ensemble data assimilation without perturbed observations. Monthly Weather Review. vol. 130, no. 7. pp. 1913-1924 (2002).

[143] N. Whiteley. Stability properties of some particle filters. The Annals of Applied Probability. vol. 23, no. 6. pp. 2500-2537 (2013).

[144] T. Yang, R.S. Laugesen, P.G. Mehta, and S.P. Meyn. Multivariable feedback particle filter. Automatica. vol. 71. pp. 10-23 (2016).

[145] C. Zhang, A. Taghvaei, and P.G. Mehta. A mean-field optimal control formulation for global optimization. IEEE Transactions on Automatic Control. vol. 64, no. 1. pp. 282-289 (2018).