\sum_{j=0} ^{m-1} W_{s_{i}, t_{j+1} } \left( W_{s_{i+1}, t_{j+1} }-W_{s_{i+1}, t_{j}}-W_{s_{i}, t_{j+1} } +W_{s_{i}, t_{j}}\right)\\
&&+  \sum_{i=0}^{m-1} \sum_{j=0} ^{m-1}\left( W_{s_{i}, t_{j+1} }-W_{s_{i}, t_{j}}\right) \left( W_{s_{i+1}, t_{j} }W_{s_{i}, t_{j}}\right).\end{aligned}$$

The first summand above usually converges to the stochastic integral with respect to the Wiener sheet $\int_{0}^{s}\int_{0}^{t} W_{u,v} dW_{u, v}$ (see [@Imk] or [@N81] for the definition of the integral and the proof of the convergence; but the stochastic integral can be also understood as the Skorohod integral $\delta \left(W _{\cdot, \cdot }1_{[0,s]\times [0,t] }(\cdot , \cdot)\right)$ with respect to the Gaussian process $W$). The summand $\sum_{i=0}^{m-1} \sum_{j=0} ^{m-1}\left( W_{s_{i}, t_{j+1} }-W_{s_{i}, t_{j}}\right) \left( W_{s_{i+1}, t_{j} }W_{s_{i}, t_{j}}\right)$ is a specific two-parameter case term and it converges, for fixed $s,t \in [0,1]$ as $m,n\to \infty$ to a random variable denoted $\tilde{M}_{s,t}$ such that the stochastic process $(\tilde{M}_{s,t})_{s,t\in [0,1]} $ is a two-parameter martingale (we refer again to [@Imk] or [@N81] for details). A similar term $\tilde{M}$ appears also in the stochastic calculus for the fractional Brownian sheet (see [@TV]). The stochastic process $\tilde{M}$ can be interpreted as $$\tilde{M}_{s,t}= \int_{0}^{s} \int_{0} ^{t} d_{u} W_{u,v} d_{v} W_{u,v}.$$ We refer to [@TV] for a discussion in this sense. In terms of the divergence integral it can 