Wavelet Analysis For Random Cascading And Random Processes

In this thesis, we start from the investigation of the so-called non-linear dynamic fluctuations in the final phase space in high energy collisions. We introduce the Harr basis wavelet transformation method and the application of this method on self-similar structure system, especially on the analysis on non-linear dynamic phenomenon in high energy multiparticle production processes.We investigate the random cascading a model, which is widely used in the analysis on the non-linear phenomenon in high energy physics. This model describe a good self-similar structure and has a good anomalous scaling behavior. So, by using the wavelet transformation study on this model, we can obtain the validity of whether the wavelet transformation method could be used in the analysis on non-linear dynamic system. By using the Ilarr wavelet basis, we do a wavelet transformation on the random cascading n model and find that the wavelet transformation keeps the scaling index of random cascade process unchanged and only times an unimportant constant factor to its sealing function.We suggest two pure random processes which do not contain any non-linear dynamic fluctuations. One has no conservation constraint of probability at any division of the phase space, which is called Model I. The other has this constraint and is called model II. We do a multircsolution analysis on these two random modelsrespectively. It is shown that the probability moment for model I is independent of division number M. There is no anomalous scaling in this model as expected for pure random process. While, beyond our expectation, for random mode! II, the probability moment is not a constant but increasing with division number M. The reason for this result comes from the constraint of probability conservation, and can be wbll understood by central limit theorem. Though the corresponding double-logarithm plot for model II is not a straight line as anomalous scaling or exact self-similar required, its noticeable upward bending behavior makes us easily confuse it with real dynamic fluctuations. At last, we perform a rnultires-olution analysis on random model II after a llarr basis wavelet transformation. We find the double-logarithm plot of probability moment versus division number M is much flatter in comparison with the results before wavelet transformation. Therefore, wavelet transformation is helpful in suppressing the fluctuations arising from non-dynamic reasons.