# American Institute of Mathematical Sciences

2009, 2009(Special): 433-441. doi: 10.3934/proc.2009.2009.433

## Sampling - reconstruction procedure with jitter of markov continuous processes formed by stochastic differential equations of the first order

 1 Av. IPN, s/n, Dept. of Telecommunications, ESIME-Zacatenco, National Polytechnic Institute of Mexico, CP 07738, Mexico DF, Mexico

Received  July 2008 Revised  July 2009 Published  September 2009

To describe sampling - reconstruction procedure (SRP) of Markov processes the conditional mean rule is used. There are two types of stochastic differential equations under consideration: 1) linear with varying in time coefficients; 2) non linear coefficients. In the first Gaussian case it is sufficiently to obtain the expression for conditional covariance function and then to calculate the reconstruction function and the error reconstruction function. In the case 2 it is necessary to obtain the solution of the corresponding Fokker - Plank - Kolmogorov equation for the conditional probability density functions (pdf). We obtain the required conditional pdf with two fixed samples and then determine the reconstruction function and the error reconstruction function. The jitter effect is described by random variable with the beta-distribution. Some examples are given.
Citation: Vladimir Kazakov. Sampling - reconstruction procedure with jitter of markov continuous processes formed by stochastic differential equations of the first order. Conference Publications, 2009, 2009 (Special) : 433-441. doi: 10.3934/proc.2009.2009.433
 [1] Selim Esedoḡlu, Fadil Santosa. Error estimates for a bar code reconstruction method. Discrete and Continuous Dynamical Systems - B, 2012, 17 (6) : 1889-1902. doi: 10.3934/dcdsb.2012.17.1889 [2] Valery Y. Glizer, Vladimir Turetsky, Emil Bashkansky. Statistical process control optimization with variable sampling interval and nonlinear expected loss. Journal of Industrial and Management Optimization, 2015, 11 (1) : 105-133. doi: 10.3934/jimo.2015.11.105 [3] Thomas Kruse, Mikhail Urusov. Approximating exit times of continuous Markov processes. Discrete and Continuous Dynamical Systems - B, 2020, 25 (9) : 3631-3650. doi: 10.3934/dcdsb.2020076 [4] Daoyi Xu, Yumei Huang, Zhiguo Yang. Existence theorems for periodic Markov process and stochastic functional differential equations. Discrete and Continuous Dynamical Systems, 2009, 24 (3) : 1005-1023. doi: 10.3934/dcds.2009.24.1005 [5] Doria Affane, Meriem Aissous, Mustapha Fateh Yarou. Almost mixed semi-continuous perturbation of Moreau's sweeping process. Evolution Equations and Control Theory, 2020, 9 (1) : 27-38. doi: 10.3934/eect.2020015 [6] Kengo Matsumoto. Cohomology groups, continuous full groups and continuous orbit equivalence of topological Markov shifts. Discrete and Continuous Dynamical Systems, 2022, 42 (2) : 841-862. doi: 10.3934/dcds.2021139 [7] Chengxiang Wang, Li Zeng. Error bounds and stability in the $l_{0}$ regularized for CT reconstruction from small projections. Inverse Problems and Imaging, 2016, 10 (3) : 829-853. doi: 10.3934/ipi.2016023 [8] Lakhdar Aggoun, Lakdere Benkherouf. A Markov modulated continuous-time capture-recapture population estimation model. Discrete and Continuous Dynamical Systems - B, 2005, 5 (4) : 1057-1075. doi: 10.3934/dcdsb.2005.5.1057 [9] Kengo Matsumoto. Continuous orbit equivalence of topological Markov shifts and KMS states on Cuntz–Krieger algebras. Discrete and Continuous Dynamical Systems, 2020, 40 (10) : 5897-5909. doi: 10.3934/dcds.2020251 [10] B. Wiwatanapataphee, Theeradech Mookum, Yong Hong Wu. Numerical simulation of two-fluid flow and meniscus interface movement in the electromagnetic continuous steel casting process. Discrete and Continuous Dynamical Systems - B, 2011, 16 (4) : 1171-1183. doi: 10.3934/dcdsb.2011.16.1171 [11] Liangliang Sun, Fangjun Luan, Yu Ying, Kun Mao. Rescheduling optimization of steelmaking-continuous casting process based on the Lagrangian heuristic algorithm. Journal of Industrial and Management Optimization, 2017, 13 (3) : 1431-1448. doi: 10.3934/jimo.2016081 [12] Keaton Hamm, Longxiu Huang. Stability of sampling for CUR decompositions. Foundations of Data Science, 2020, 2 (2) : 83-99. doi: 10.3934/fods.2020006 [13] Alexandre J. Chorin, Fei Lu, Robert N. Miller, Matthias Morzfeld, Xuemin Tu. Sampling, feasibility, and priors in data assimilation. Discrete and Continuous Dynamical Systems, 2016, 36 (8) : 4227-4246. doi: 10.3934/dcds.2016.36.4227 [14] Shixu Meng. A sampling type method in an electromagnetic waveguide. Inverse Problems and Imaging, 2021, 15 (4) : 745-762. doi: 10.3934/ipi.2021012 [15] Tim Kreutzmann, Andreas Rieder. Geometric reconstruction in bioluminescence tomography. Inverse Problems and Imaging, 2014, 8 (1) : 173-197. doi: 10.3934/ipi.2014.8.173 [16] Jiaqing Yang, Bo Zhang, Ruming Zhang. Reconstruction of penetrable grating profiles. Inverse Problems and Imaging, 2013, 7 (4) : 1393-1407. doi: 10.3934/ipi.2013.7.1393 [17] Jorge Tejero. Reconstruction of rough potentials in the plane. Inverse Problems and Imaging, 2019, 13 (4) : 863-878. doi: 10.3934/ipi.2019039 [18] Felipe Ponce-Vanegas. Reconstruction of the derivative of the conductivity at the boundary. Inverse Problems and Imaging, 2020, 14 (4) : 701-718. doi: 10.3934/ipi.2020032 [19] Peter Monk, Virginia Selgas. Sampling type methods for an inverse waveguide problem. Inverse Problems and Imaging, 2012, 6 (4) : 709-747. doi: 10.3934/ipi.2012.6.709 [20] Fang Zeng. Extended sampling method for interior inverse scattering problems. Inverse Problems and Imaging, 2020, 14 (4) : 719-731. doi: 10.3934/ipi.2020033

Impact Factor: