  Our simple but useful technique is using an integration by parts to split the
stochastic convolution into two terms. We develop five applications for this
technique. The first one is getting a uniform estimate of stochastic
convolution of $\alpha$-stable processes. Since $\alpha$-stable noises only
have $p<\alpha$ moment, unlike the stochastic convolution of Wiener process,
the well known Da Prato-Kwapie\'n-Zabczyk's factorization ([5]) is not
applicable. Alternatively, combining this technique with Doob's martingale
inequality, we obtain a uniform estimate similar to that of stochastic
convolution of Wiener process. Using this estimate, we show that the stochastic
convolution of $\alpha$-stable noises stays, with positive probability, in
arbitrary small ball with zero center. These two results are important for
studying ergodicity and regularity of stochastic PDEs forced by $\alpha$-stable
noises ([9]). The third application is getting the same results as in [12]. The
fourth one gives the trajectory regularity of stochastic Burgers equation
forced by $\alpha$-stable noises ([9]). Finally, applying a similar integration
by parts to stochastic convolution of Wiener noises, we get the uniform
estimate and continuity property originally obtained by Da
Prato-Kwapie\'n-Zabczyk's factorization.
