On Marginal Processes of Quadratic Stochastic Processes

Abstract

It is known that the theory of Markov processes is a rapidly developing field with numerous applications to many branches of mathematics and physics, biology, and so on. But there are some physical models which cannot be described by such processes. One of such models is related to population genetics. These processes are called quadratic stochastic processes (q.s.p.). In the present paper, we associate to given q.s.p. two kind of processes, which call marginal processes. Note that one of them is Markov process. We prove that such kind of processes uniquely define q.s.p. Moreover, we provide a construction of nontrivial examples of q.s.p. Weak ergodicity of q.s.p. is also studied in terms of the marginal processes.