# 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
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