Sampling - reconstruction procedure with jitter of markov continuous
processes formed by stochastic differential equations of the first
order
Vladimir Kazakov - Av. IPN, s/n, Dept. of Telecommunications, ESIME-Zacatenco, National Polytechnic Institute of Mexico, CP 07738, Mexico DF, Mexico (email) Abstract: 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: Sampling - reconstruction, Markov continuous process, error, jitter
Received: July 2008; Revised: July 2009; Published: September 2009. |