On moduli of continuity for a two-parameter Ornstein-Uhlenbeck process (Q1804742)

Consider a two-parameter Ornstein-Uhlenbeck process \(X(t,v)\) defined by \[ X(t,v) = e^{- \alpha t - \beta v}\left\{X_ 0 + \int^ t_ 0 \int^ v_ 0 e^{\alpha x + \beta y} dW (x,y)\right\}, \] where \(W\) is a two-parameter Brownian motion, \(X_ 0\) is a random variable independent of \(W\), \(\alpha > 0\), \(\beta > 0\). Lévy's exact moduli of continuity of this process are established not only for one of two parameters but also for both parameters.