Planning of experiments for a nonautonomous ornstein-uhlenbeck process

[1] ALLEN, E.: Modeling with It¯o Stochastic Differential Equations. Springer, Dordrecht, 2007.Search in Google Scholar

[2] ARNOLD, L.: Stochastic Differential Equations: Theory and Applications. John Wiley & Sons, New York, 1974.Search in Google Scholar

[3] HARMAN, R.-ˇSTULAJTER, F.: Optimality of equidistant sampling designs for a non- stationary Ornstein-Uhlenbeck process, in: Proc. of the 6th St. Petersburg Workshop on Simulation, Vol. 2 (S. M. Ermakov et al. eds.), St. Petersburg State University, St. Pe- tersburg, 2009, pp. 1097-1101.Search in Google Scholar

[4] HARMAN, R.-ˇ STULAJTER, F.: Optimal sampling designs for the Brownian motion with a quadratic drift, J. Statist. Plann. Inference 141 (2011), 2750-2758.10.1016/j.jspi.2011.02.025Search in Google Scholar

[5] HARMAN, R.-ˇ STULAJTER, F.: Optimal sampling designs for a two-parametric Ornstein-Uhlenbeck process (submitted).Search in Google Scholar

[6] IT¯O, K.: On a formula concerning stochastic differentials, Nagoya Math. J. 3 (1951), 55-65.10.1017/S0027763000012216Search in Google Scholar

[7] KISEL’´AK, J.-STEHL´IK,M.: Equidistant and D-optimal designs for parameters of Orn- stein-Uhlenbeck process, Statist. Probab. Lett. 78 (2008), 1388-1396.10.1016/j.spl.2007.12.012Search in Google Scholar

[8] KUNZE, M.-LORENZI, L.-LUNARDI, A.: Nonautonomous Kolmogorov parabolic equ- ations with unbounded coefficients, Trans. Amer. Math. Soc. 362 (2010), 169-198.10.1090/S0002-9947-09-04738-2Search in Google Scholar

[9] LEMONS, D. S.: An Introduction to Stochastic Processes in Physics. Johns Hopkins University Press, Baltimore, 2002.Search in Google Scholar

[10] MUKHERJEE, B.: Exactly optimal sampling designs for processes with a product covari- ance structure, Canad. J. Statist. 31 (2003), 69-87.10.2307/3315904Search in Google Scholar

[11] ØKSENDAL, B.: Stochastic Differential Equations: An Introduction with Applications (6th ed.), Springer, Berlin, 2003.10.1007/978-3-642-14394-6_1Search in Google Scholar

[12] P´AZMAN, A.: Foundations of Optimum Experimental Design. Riedel, Dordrecht, 1986.Search in Google Scholar

[13] P´AZMAN, A.: Nonlinear Statistical Models. Kluwer, Dordrecht, 1993.10.1007/978-94-017-2450-0Search in Google Scholar

[14] PUKELSHEIM, F.: Optimal Design of Experiments. John Wiley & Sons, New York, 1993.Search in Google Scholar

[15] RICCARDI, L. M.-SACERDOTE, L.: The Ornstein-Uhlenbeck process as a model for neuronal activity. Biol. Cybern. 35 (1979), 1-9.Search in Google Scholar

[16] SACKS, J.-YLVISAKER, D.: Designs for regression problems with correlated errors. Ann. Math. Stat. 37 (1966), 66-89.Search in Google Scholar

[17] SACKS, J.-YLVISAKER, D.: Designs for regression problems with correlated errors: many parameters, Ann. Math. Stat. 39 (1968), 49-69.10.1214/aoms/1177698504Search in Google Scholar

[18] SACKS, J.-YLVISAKER, D.: Designs for regression problems with correlated errors III, Ann. Math. Stat. 41 (1970), 2057-2074.10.1214/aoms/1177696705Search in Google Scholar

[19] SCHUSS, Z.: Theory and Applications of Stochastic Processes: An Analytical Approach. Springer, New York, 2010.10.1007/978-1-4419-1605-1Search in Google Scholar

[20] ZAGORAIOU, M.-ANTOGNINI, A. B.: Optimal designs for parameter estimation of the Ornstein-Uhlenbeck process, Appl. Stoch. Models Bus. Ind. 25 (2009), 583-600.10.1002/asmb.749Search in Google Scholar