We show that the processes described by Avrami functions are self-similar. A comparative function characterizes a self-similar process by a certain Avrami exponent. We define the self-similar categories of some well-k...We show that the processes described by Avrami functions are self-similar. A comparative function characterizes a self-similar process by a certain Avrami exponent. We define the self-similar categories of some well-known biological processes. The method to determine the Avrami exponent by choosing the comparative function is demonstrated on the diffusion model of the growth of nuclei. We generalize the results.展开更多
Let X= (Ω, ■, ■_t, X_t,, θ_t, p~x) be a self-similar Markov process on (0,∞) with non-decreasing path. The exact Hausdorff and Packing measure functions of the image X([0,t] ) are obtained.
The anthem investigate the hitting probability, polarity and the relationship between the polarity and Hausdorff dimension for self-similar Markov processes with state space (0, infinity) and increasing path.
By using Lamperti＇s bijection between self-similar Markov processes and L@vy processes~ we prove finiteness of moments and asymptotic behavior of passage times for increasing self-similar Markov processes valued in ...By using Lamperti＇s bijection between self-similar Markov processes and L@vy processes~ we prove finiteness of moments and asymptotic behavior of passage times for increasing self-similar Markov processes valued in （0, ~）. We Mso investigate the behavior of the process when it crosses a level. A limit theorem concerning the distribution of the process immediately before it crosses some level is proved. Some useful examples are given.展开更多
Yamamuro in [1] defines strong and weak transience of Markov processes; gives a criterion for strong transience of Feller processes; and further, discusses strong and weak transience of Ornstein-Uhlenbeck type process...Yamamuro in [1] defines strong and weak transience of Markov processes; gives a criterion for strong transience of Feller processes; and further, discusses strong and weak transience of Ornstein-Uhlenbeck type processes. In this article, the authors weaken the Feller property of the result in [1] to weak Feller property and discuss the strong transience of operator-self-similar Markov processes.展开更多
This paper considers a special class of operator self-similar processes Markov processes {X（t）, t≥0} with independent self-similar components, that is, X （ t ） =（X^1（t）,…,X^d（t））, where {X^i（t）,t≥0}, i=...This paper considers a special class of operator self-similar processes Markov processes {X（t）, t≥0} with independent self-similar components, that is, X （ t ） =（X^1（t）,…,X^d（t））, where {X^i（t）,t≥0}, i=1,2,…,d are d independent real valued self-similar Markov processes. By means of Brel-Cantelli lemma, we give two results about asymptotic property as t→∞ of sample paths for two special classes of Markov processes with independent self-similar components.展开更多
The alpha stable self-similar stochastic process has been proved an effective model for high variable data traffic. A deep insight into some special issues and considerations on use of the process to model aggregated ...The alpha stable self-similar stochastic process has been proved an effective model for high variable data traffic. A deep insight into some special issues and considerations on use of the process to model aggregated VBR video traffic is made. Different methods to estimate stability parameter a and self-similar parameter H are compared. Processes to generate the linear fractional stable noise （LFSN） and the alpha stable random variables are provided. Model construction and the quantitative comparisons with fractional Brown motion （FBM） and real traffic are also examined. Open problems and future directions are also given with thoughtful discussions.展开更多
The paper focuses on measuring self-similarity using few techniques by an index called Hurst index which is a self-similarity parameter. It has been evident that Internet traffic exhibits self-similarity. Motivated by...The paper focuses on measuring self-similarity using few techniques by an index called Hurst index which is a self-similarity parameter. It has been evident that Internet traffic exhibits self-similarity. Motivated by this fact, real time web users at various centers considered here as traffic and it has been examined by various methods to test the self-similarity. The results from the experiments carried out verify that the traffic examined in the present study is self similar using a new method based on some descriptive measures;for example percentiles have been applied to compute Hurst parameter which gives intensity of the self-similarity. Numerical results and analysis we discussed and presented here play a significant role to improve the services at web centers in the view of quality of service (QOS).展开更多
Recent empirical studies of the real traffic measurement show that the traditional traffic models cannot capture the character of long-range dependence of the traffic. And many computer simulations said that this char...Recent empirical studies of the real traffic measurement show that the traditional traffic models cannot capture the character of long-range dependence of the traffic. And many computer simulations said that this character has large influences on the network performance. So fractal or self-similar models are more suitable to describe the modern traffic. But there is still little known about the performance of the multiplexer under self-similar traffic. In this paper, a quasi-self-similar traffic model (QSSP) is proposed. Using this model, the upper bond of the cell loss rate and multiplexing gain of the multiplexer are gotten when there are N i.i.d. QSSP inputs. If the sources have different parameters, an efficient numerical algorithm to get, this bond is proposed. Simulations indicate that our analysis is correct and accurate.展开更多
This article explores the short-range dependence （SRD） and the long-range dependence （LRD） of self-similar traffic generated by the fractal-binomial-noise-driven Poisson process （FBNDP） model and lays emphasis o...This article explores the short-range dependence （SRD） and the long-range dependence （LRD） of self-similar traffic generated by the fractal-binomial-noise-driven Poisson process （FBNDP） model and lays emphasis on the former. By simulation, the SRD decaying trends with the increase of Hurst value and peak rate are obtained, respectively. After a comprehensive analysis of accuracy of self-similarity intensity, the optimal range of peak rate is determined by taking into account the time cost, the accuracy of self-similarity intensity, and the effect of SRD.展开更多
文摘We show that the processes described by Avrami functions are self-similar. A comparative function characterizes a self-similar process by a certain Avrami exponent. We define the self-similar categories of some well-known biological processes. The method to determine the Avrami exponent by choosing the comparative function is demonstrated on the diffusion model of the growth of nuclei. We generalize the results.
基金the National Natural Science Foundation of China
文摘Let X= (Ω, ■, ■_t, X_t,, θ_t, p~x) be a self-similar Markov process on (0,∞) with non-decreasing path. The exact Hausdorff and Packing measure functions of the image X([0,t] ) are obtained.
基金the National Natural Science Foundation of China and the StateEducation of Commission Ph.D. Station Foundation
文摘The anthem investigate the hitting probability, polarity and the relationship between the polarity and Hausdorff dimension for self-similar Markov processes with state space (0, infinity) and increasing path.
基金supported in part by the National Natural Science Foundation of China(1117126211171263)
文摘By using Lamperti＇s bijection between self-similar Markov processes and L@vy processes~ we prove finiteness of moments and asymptotic behavior of passage times for increasing self-similar Markov processes valued in （0, ~）. We Mso investigate the behavior of the process when it crosses a level. A limit theorem concerning the distribution of the process immediately before it crosses some level is proved. Some useful examples are given.
基金Research supported in part by the National Natural Science Foundation of China and a grant from the Ministry of Education of China
文摘Yamamuro in [1] defines strong and weak transience of Markov processes; gives a criterion for strong transience of Feller processes; and further, discusses strong and weak transience of Ornstein-Uhlenbeck type processes. In this article, the authors weaken the Feller property of the result in [1] to weak Feller property and discuss the strong transience of operator-self-similar Markov processes.
文摘This paper considers a special class of operator self-similar processes Markov processes {X（t）, t≥0} with independent self-similar components, that is, X （ t ） =（X^1（t）,…,X^d（t））, where {X^i（t）,t≥0}, i=1,2,…,d are d independent real valued self-similar Markov processes. By means of Brel-Cantelli lemma, we give two results about asymptotic property as t→∞ of sample paths for two special classes of Markov processes with independent self-similar components.
文摘The alpha stable self-similar stochastic process has been proved an effective model for high variable data traffic. A deep insight into some special issues and considerations on use of the process to model aggregated VBR video traffic is made. Different methods to estimate stability parameter a and self-similar parameter H are compared. Processes to generate the linear fractional stable noise （LFSN） and the alpha stable random variables are provided. Model construction and the quantitative comparisons with fractional Brown motion （FBM） and real traffic are also examined. Open problems and future directions are also given with thoughtful discussions.
文摘The paper focuses on measuring self-similarity using few techniques by an index called Hurst index which is a self-similarity parameter. It has been evident that Internet traffic exhibits self-similarity. Motivated by this fact, real time web users at various centers considered here as traffic and it has been examined by various methods to test the self-similarity. The results from the experiments carried out verify that the traffic examined in the present study is self similar using a new method based on some descriptive measures;for example percentiles have been applied to compute Hurst parameter which gives intensity of the self-similarity. Numerical results and analysis we discussed and presented here play a significant role to improve the services at web centers in the view of quality of service (QOS).
文摘Recent empirical studies of the real traffic measurement show that the traditional traffic models cannot capture the character of long-range dependence of the traffic. And many computer simulations said that this character has large influences on the network performance. So fractal or self-similar models are more suitable to describe the modern traffic. But there is still little known about the performance of the multiplexer under self-similar traffic. In this paper, a quasi-self-similar traffic model (QSSP) is proposed. Using this model, the upper bond of the cell loss rate and multiplexing gain of the multiplexer are gotten when there are N i.i.d. QSSP inputs. If the sources have different parameters, an efficient numerical algorithm to get, this bond is proposed. Simulations indicate that our analysis is correct and accurate.
基金This study is supported by National Natural Science Foundation of China(60507007,60372100).
文摘This article explores the short-range dependence （SRD） and the long-range dependence （LRD） of self-similar traffic generated by the fractal-binomial-noise-driven Poisson process （FBNDP） model and lays emphasis on the former. By simulation, the SRD decaying trends with the increase of Hurst value and peak rate are obtained, respectively. After a comprehensive analysis of accuracy of self-similarity intensity, the optimal range of peak rate is determined by taking into account the time cost, the accuracy of self-similarity intensity, and the effect of SRD.
