A study on marginal Markov processes and construction of quadratic stochastic processes - Nurul Akma binti Supar (Kulliyah of Science, International islamic University Malaysia, 2014)
This research focused on quadratic stochastic processes. In this work, we define two kinds of processes by means of given quadratic stochastic process. It is shown such processes are Markov and relate to each other by certain rule. The findings of study show that how quadratic stochastic processes and Markov processes relate to each other, and allow to produce interesting examples quadratic stochastic processes by means of Markov processes. It is known that construction of non-trivial examples of quadratic stochastic processes is important. Therefore, we give a construction of quadratic stochastic processes through two given processes. Moreover, in this research we also find corresponding marginal Markov processes. It is also produced differential equations which define non-homogeneous quadratic stochastic processes. As an illustration of the use of marginal processes, in this thesis we study weak ergodicity of quadratic stochastic processes by means of the Markov processes.