American Institute of Mathematical Sciences

Advanced
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

Vladimir Kazakov 1,

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.
Keywords: Markov continuous process, error, Sampling - reconstruction, jitter.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.
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]

Valery Y. Glizer, Vladimir Turetsky, Emil Bashkansky. Statistical process control optimization with variable sampling interval and nonlinear expected loss. Journal of Industrial & Management Optimization, 2015, 11 (1) : 105-133. doi: 10.3934/jimo.2015.11.105
[2]

Selim Esedoḡlu, Fadil Santosa. Error estimates for a bar code reconstruction method. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 1889-1902. doi: 10.3934/dcdsb.2012.17.1889
[3]

Daoyi Xu, Yumei Huang, Zhiguo Yang. Existence theorems for periodic Markov process and stochastic functional differential equations. Discrete & Continuous Dynamical Systems - A, 2009, 24 (3) : 1005-1023. doi: 10.3934/dcds.2009.24.1005
[4]

Chengxiang Wang, Li Zeng. Error bounds and stability in the $l_{0}$ regularized for CT reconstruction from small projections. Inverse Problems & Imaging, 2016, 10 (3) : 829-853. doi: 10.3934/ipi.2016023
[5]

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 & Continuous Dynamical Systems - B, 2011, 16 (4) : 1171-1183. doi: 10.3934/dcdsb.2011.16.1171
[6]

Liangliang Sun, Fangjun Luan, Yu Ying, Kun Mao. Rescheduling optimization of steelmaking-continuous casting process based on the Lagrangian heuristic algorithm. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1431-1448. doi: 10.3934/jimo.2016081
[7]

Lakhdar Aggoun, Lakdere Benkherouf. A Markov modulated continuous-time capture-recapture population estimation model. Discrete & Continuous Dynamical Systems - B, 2005, 5 (4) : 1057-1075. doi: 10.3934/dcdsb.2005.5.1057
[8]

Alexandre J. Chorin, Fei Lu, Robert N. Miller, Matthias Morzfeld, Xuemin Tu. Sampling, feasibility, and priors in data assimilation. Discrete & Continuous Dynamical Systems - A, 2016, 36 (8) : 4227-4246. doi: 10.3934/dcds.2016.36.4227
[9]

Peter Monk, Virginia Selgas. Sampling type methods for an inverse waveguide problem. Inverse Problems & Imaging, 2012, 6 (4) : 709-747. doi: 10.3934/ipi.2012.6.709
[10]

Martin Hanke. Why linear sampling really seems to work. Inverse Problems & Imaging, 2008, 2 (3) : 373-395. doi: 10.3934/ipi.2008.2.373
[11]

T. Hillen, K. Painter, Christian Schmeiser. Global existence for chemotaxis with finite sampling radius. Discrete & Continuous Dynamical Systems - B, 2007, 7 (1) : 125-144. doi: 10.3934/dcdsb.2007.7.125
[12]

Tim Kreutzmann, Andreas Rieder. Geometric reconstruction in bioluminescence tomography. Inverse Problems & Imaging, 2014, 8 (1) : 173-197. doi: 10.3934/ipi.2014.8.173
[13]

Jiaqing Yang, Bo Zhang, Ruming Zhang. Reconstruction of penetrable grating profiles. Inverse Problems & Imaging, 2013, 7 (4) : 1393-1407. doi: 10.3934/ipi.2013.7.1393
[14]

Ummugul Bulut, Edward J. Allen. Derivation of SDES for a macroevolutionary process. Discrete & Continuous Dynamical Systems - B, 2013, 18 (7) : 1777-1792. doi: 10.3934/dcdsb.2013.18.1777
[15]

Jiying Liu, Jubo Zhu, Fengxia Yan, Zenghui Zhang. Compressive sampling and $l_1$ minimization for SAR imaging with low sampling rate. Inverse Problems & Imaging, 2013, 7 (4) : 1295-1305. doi: 10.3934/ipi.2013.7.1295
[16]

Horst Heck, Gunther Uhlmann, Jenn-Nan Wang. Reconstruction of obstacles immersed in an incompressible fluid. Inverse Problems & Imaging, 2007, 1 (1) : 63-76. doi: 10.3934/ipi.2007.1.63
[17]

Mila Nikolova. Model distortions in Bayesian MAP reconstruction. Inverse Problems & Imaging, 2007, 1 (2) : 399-422. doi: 10.3934/ipi.2007.1.399
[18]

Jingzhi Li, Hongyu Liu, Qi Wang. Fast imaging of electromagnetic scatterers by a two-stage multilevel sampling method. Discrete & Continuous Dynamical Systems - S, 2015, 8 (3) : 547-561. doi: 10.3934/dcdss.2015.8.547
[19]

Tian Xiang. On effects of sampling radius for the nonlocal Patlak-Keller-Segel chemotaxis model. Discrete & Continuous Dynamical Systems - A, 2014, 34 (11) : 4911-4946. doi: 10.3934/dcds.2014.34.4911
[20]

Jingzhi Li, Jun Zou. A direct sampling method for inverse scattering using far-field data. Inverse Problems & Imaging, 2013, 7 (3) : 757-775. doi: 10.3934/ipi.2013.7.757

 Impact Factor: 

Tools

Metrics

  • PDF downloads (7)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2018 American Institute of Mathematical Sciences