simulating stohastic process with a monophyletic random vectorsimulating stoc.docVIP

Simulating stochastic process with a monophyletic random vector Tang Baoxin Cheng Kaihua Department of Civil Engineering, Yangzhou University, Jiangsu 225127 China tbx001@163.com Abstract: The large number of basic random variables in stochastic process, cause great troubles for calculation and analysis. Based on twice orthogonal expansion in the stochastic process and the expression of uncorrelated random vectors by use of orthogonal functions originate from a single source random variable, a method of triple orthogonal expansion for a stochastic process is put forward ,which can simulate a stochastic process with only one random variable. Example calculation shows the effectiveness of the monophyletic analysis method (MAM).This method can be applied for the other stochastic analysis based on the correlation theory. Keywords: monophyletic; random vector; stochastic process; orthogonal expansion; simulation When Housner proposed the simulation on the specific spectral characteristics of earthquake motions[1] using random point pulse sequences since 1947, many scholars conducted extensive study on random earthquake motions[2]. The simulation of earthquake motion can be divided into two categories clearly: Seismological methods and Earthquake engineering methods[3]. The former focus on the simulations of the earthquake source mechanism and the physical processes. The latter is a random process of abstraction of ground motion, and on the basis of stable and ergodic assumption, established the power spectrum of the empirical model which can reflect the second-order statistical properties of ground motion. The Karhunen-Loeve (K-L) decomposition method analyzed stochastic process from the perspective of a collection of random variables[4]. China scholars Li Jie further proposed a second orthogonal expansion method on the basis of K-L decomposition method[5]. This paper proposes the Monophyletic Analysis Method（MAM）.Based on twice orthogonal expansion in the stochastic p