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The LISDLG process denoted by $J\left(t\right)$ is defined in Iglói and Terdik [ESAIM: PS 7 (2003) 23–86] by a functional limit theorem as the limit of ISDLG processes. This paper gives a more general limit representation of $J\left(t\right)$. It is shown that process $J\left(t\right)$ has its own renormalization group and that $J\left(t\right)$ can be represented as the limit process of the renormalization operator flow applied to the elements of some set of stochastic processes. The latter set consists of IGSDLG processes which are generalizations of the ISDLG...

The LISDLG process denoted by is defined in Iglói and Terdik [ (2003) 23–86] by a functional limit theorem as the limit of ISDLG processes. This paper gives a more general limit representation of . It is shown that process has its own renormalization group and that can be represented as the limit process of the renormalization operator flow applied to the elements of some set of stochastic processes. The latter set consists of IGSDLG processes which are generalizations of the...

We study Karhunen-Loève expansions of the process(X t(α))t∈[0,T) given by the stochastic differential equation $$d{X}_t^{\left(\alpha \right)}=-\frac{\alpha }{T-t}{X}_t^{\left(\alpha \right)}dt+d{B}_t,t\in [0,T)$$ , with the initial condition X 0(α) = 0, where α > 0, T ∈ (0, ∞), and (B t)t≥0 is a standard Wiener process. This process is called an α-Wiener bridge or a scaled Brownian bridge, and in the special case of α = 1 the usual Wiener bridge. We present weighted and unweighted Karhunen-Loève expansions of X (α). As applications, we calculate the Laplace transform and the distribution function...

In this paper a new multifractal stochastic process called Limit of the Integrated Superposition of Diffusion processes with Linear differencial Generator (LISDLG) is presented which realistically characterizes the network traffic multifractality. Several properties of the LISDLG model are presented including long range dependence, cumulants, logarithm of the characteristic function, dilative stability, spectrum and bispectrum. The model captures higher-order statistics by the cumulants. The relevance...