This thesis is based on my published work during the master phase. Gravitational wave science is in new age with  the help of the development of many other subjects and the progress of technology, taking more attentions of many scientists. Stochastic gravitational wave background is one target of current gravitational wave detection. Detecting and analyzing  the stochastic gravitational wave background need skillful data analyze technic with knowing the sources well. The correlation of two data streams from two different detectors is the key of analyzing this kind of source. Using a network of combining multiple detectors to improve the detection ability is a natural idea. Two approaches have been proposed: (i)correlating the outputs of a pair of detectors, then combing the multiple pairs, and (ii) directly combing the outputs of $2N$ detectors. As several large scale interferometers are in operation, it is necessary to compare those two approaches. Stochastic gravitational wave background  has two origins: an extremely large number of weak astrophysical gravitational wave sources (forming astrophysical stochastic gravitational wave background), and some processes of very early universe (forming primordial stochastic gravitational wave background ).It is of great significance to research the primordial stochastic gravitational wave background due to its carrying unique information of very early universe. In all cosmology theories, string cosmology predicts an interesting energy density spectrum which grows rapidly with frequency. This means that the ground laser interferometer  may be the best detector. We show the certain ranges of the parameters of string cosmology model. The result indicates that, for the real detectors (LIGO、Virgo and GEO),  i)the network of multiple pairs of real laser interferometers does improve the detection ability of the string cosmology gravitational wave background, ii) the approach of combining multiple pairs of laser interferometers is better than the approach of directly combining the outputs of multiple laser interferometers. We also introduce the detection methods for gravitational wave burst and periodical gravitational wave.