Project supported by the National Natural Science Foundation of China
Using the plot of growing single-parameter Markov processes on a single-parameter Markov process, we constructed successfully a class of important two-parameter processes which are called MM-class processes and whose ...
Let (Ω,(?), P) be a complete probability space with a family of sub-σ-fields {(?)_z}_z∈R_+~2 which satisfies the usual conditions. Yeh considered the existence and uniqueness of strong solutions of the following no...
Ⅰ. INTRODUCTION AND DEFINITIONS When we consider different pasts, there are various definitions of Markov properties for twoparameter processes. Even if we only consider the wide-past, there are still several definit...
Given (Ω, (?), P ), let ∧ be a nonnegative additional set function on R_+~2 and have density function λ about Lebesgue measure l. For simplicity, in this report, we always suppose that there exists a constant M>...
I. INTRODUCTION AND DEFINITIONS In this report, we shall give a simple counterexample to negative Theorem 1 and Proposition 3 (c)(ii)in [1] and explain the difference between the large-past Markov property and *-Marko...
Let z(u, v) be a point on the plane, R+2=(z:u≥0, v≥0). B+2 represents the Borel field in R+2. X={x(z, ω), z∈R+2} the stochastic process on some probability space (Ω, F, P). We say that X is a two-paramete...
A real-valued stochastic process X={X(s, t), s≥0, t≥0} is a two-parameter Ornstein-Uhlenbeck process (OUP2) if, where α>0, β>0, σ>0 are constants, W is Brownian sheet, and X(0, 0) is random variable,