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Long-Memory Dependence Statistical Models for DDoS Attacks Detection

Andrysiak T., Saganowski Ł., Maszewski M., Grad P.

Image Processing & Communications

2015

Vol. 20, no. 4

31--40

DDoS attacks detection method based on modelling the variability with the use of conditional average and variance in examined time series is proposed in this article. Variability predictions of the analyzed network traffic are realized by estimated statistical models with long-memory dependence ARFIMA, Adaptive ARFIMA, FIGARCH and Adaptive FIGARCH. We propose simple parameter estimation models with the use of maximum likelihood function. Selection of sparingly parameterized form of the models is realized by means of information criteria representing a compromise between brevity of representation and the extent of the prediction error. In the described method we propose using statistical relations between the forecasted and analyzed network traffic in order to detect abnormal behavior possibly being a result of a network attack. Performed experiments confirmed effectiveness of the analyzed method and cogency of the statistical models.

Probabilistic solution to a two-dimensional LQG homing problem

Makasu C., Lefebvre M.

Control and Cybernetics

2012

Vol. 41, no. 1

5-12

Let xt be an arbitrary one-dimensional diffusion process and yt be a one-dimensional controlled diffusion process starting from y0 = y ∈ (a, b). The process is controlled until yt crosses either y = a or y = b for the first time. Our aim is to find the control ut that minimizes an expected cost functional with both quadratic control and boundary crossing costs. An explicit form for the optimal control is obtained under certain conditions.