Stochastic processes are approved presentation of real systems which its development in space or time can be supposed as random. A semi-hidden Markov model as a type of stochastic processes is a modification of hidden Markov models with states that are no longer totally unobservable and are less hidden. This mathematical model is employed for modeling data sequences with long runs, memory and statistical inertia. In this article, we investigate the theory of the semi-hidden Markov model along with its parameter estimation and order estimation methods. Moreover, the proposed model is applied to model the error traces generated by the wireless channels. A new Markov-based trace analysis algorithm is suggested to divide a non-stationary network error trace into stationary parts. By means of the best semi-hidden Markov model and fitting probability distribution, we would be able to model these parts accurately. Calculating the information measure criteria and the autocorrelation function by running the modified Baum-Welch algorithm several times help us to find the optimal order of the semi-hidden Markov model.
CDMA is an important and basic part of today's communications technologies. This technology can be analyzed efficiently by reducing the time, computation burden, and cost by characterizing the physical layer with a Markov Model. Waveform level simulation is generally used for simulating different parts of a digital communication system. In this paper, we introduce two different mathematical methods to model digital communication channels. Hidden Markov and Semi Hidden Markov models' applications have been investigated for evaluating the DS-CDMA link performance with different parameters. Hidden Markov Models have been a powerful mathematical tool that can be applied as models of discrete-time series in many fields successfully. A semi-hidden Markov model as a stochastic process is a modification of hidden Markov models with states that are no longer unobservable and less hidden. A principal characteristic of this mathematical model is statistical inertia, which admits the generation, and analysis of observation symbol contains frequent runs.
Semi-Markov processes can be considered as a generalization of both Markov and renewal processes. One of the principal characteristics of these processes is that in opposition to Markov models, they represent systems whose evolution is dependent not only on their last visited state but on the elapsed time since this state. Semi-Markov processes are replacing the exponential distribution of time intervals with an optional distribution. In this paper, we give a statistical approach to test the semi-Markov hypothesis. Moreover, we describe a Monte Carlo algorithm able to simulate the trajectories of the semi-Markov chain. This simulation method is used to test the semi-Markov model by comparing and analyzing the results with empirical data. We introduce the database of Network traffic which is employed for applying the Monte Carlo algorithm. The statistical characteristics of real and synthetic data from the models are compared. The comparison between the semi-Markov and the Markov models is done by computing the Autocorrelation functions and the probability density functions of the Network traffic real and simulated data as well. All the comparisons admit that the Markovian hypothesis is rejected in favor of the more general semi Markov one. Finally, the interval transition probabilities which show the future predictions of the Network traffic are given.
Grey model can be counted as a potent approximation for extracting system dynamic information with only small amount of data. A weighted Markov model is appropriate for predicting the stochastic fluctuating dynamic by a transition probability matrix and normalizing autocorrelation coefficient as weighted and a single gene system cloud grey SCGM(1,1)c model. It is applied to regulate the development trend of time series. In this paper we employed a weighted Markov SCGM(1,1)c model for predicting the Gold/Oil ,DJIA/Gold and USD/XAU ratios. By examining the forecasted results, it was concluded that the weighted Markov SCGM(1,1)c model is a reliable and effective modeling method.
The Markov order is a crucial measure of the memory of a process and its information is essential for appropriate simulation of aspects of the process. In this paper we suggest a robust and straightforward exact significance test based on generating surrogate data to assess the Markov order of a time series. This method is valid for any sample size and certifies a uniform sampling from the set of sequences that definitely have the nth order characteristics of the observed data. The Markov property and order of IEEE802.11a errors are investigated using this test.
Highlights• A new mathematical stochastic method for predicting the future signal fading is introduced.• The elements of the Semi Markov Model are presented.• The forecasting of the fading occurrences in dimensions of time and amplitude together is performed.• The occurrences of deep fades are forecasted for the next 1 to 21 unit times.
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