ON THE ALMOST SURELY ASYMPTOTIC BOUNDS OF A CLASS OF ORNSTEIN-UHLENBECK PROCESSES IN INFINITE DIMENS

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Given a real-valued separable M-type 2 Banach space X with the p-th power of the norm of C2-class, the almost sure asymptotic upper bounds of the solutions of the stein-Uhlenbeck Processes described by the following equations{dz(t) = A(t, z(t)) dt+σ(t, z(t)) dW(t),z(O) = zo ∈ X,are investigated. This study generalizes the corresponding well-known finite dimensional results of Lapeyre (1989) and Mao (1992).
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