PROPAGATION OF SINGULARITIES IN THE ORNSTEIN-UHLENBECK PROCESSES WITH TWO PARAMETERS

\tau_\text Let X(s, t)=e^-\alpha t-\beta t\leftX_0+\sigma \int_0^s \int_0^t e^\alpha a+\beta b d W(a, b)\right be an Ornstein-Uhlenbeck process with two parameters \left(\mathrmOUP_2\right). In this paper, we prove that each section X_0 \Rightarrow X(s, c) is an ollP. We also discuss the law of iterated logrithm of \mathrmOUP_2. A point s is oalled a singularity of \mathrmOUP_2 X(s, t) if \lim _h \nmid 0 \sup \frac|X(s+h, t)-X(s, t)|\sqrth \log \log 1 / h=+\infty. We point out that the singularities can propagate parallelly to the ooordinate axis just as in the Brownian sheet.