Theory and Modern Applications
No. | t | ρ(t) | ϕ(t) | φ(t) |
---|---|---|---|---|
1 | \(\bullet _{i}\) | 0.5 | \(W_{i}(h)\) | \(\int _{0}^{1}z_{\tau}^{(i)}\,\mathrm{d}\tau \) |
2 | 1 | \(W_{0}(h)=h\) | \(\int _{0}^{1}z_{\tau}^{(0)}\,\mathrm{d}\tau \) | |
3 | 1 | \(\int _{0}^{h}W_{j}(s)\circ \mathrm{d}W_{i}(s)\) | \(\int _{0}^{1}z_{\tau}^{(i)} \int _{0}^{1}Z_{\tau ,\xi}^{(j)}\,\mathrm{d}\xi \,\mathrm{d}\tau \) | |
4 | 1.5 | \(\int _{0}^{1}W_{j}(s)W_{k}(s)\circ \mathrm{d}W_{i}(s)\) | \(\int _{0}^{1}z_{\tau}^{(i)}\int _{0}^{1}Z_{\tau ,\xi}^{(j)}\,\mathrm{d}\xi \int _{0}^{1}Z_{\tau ,\varsigma}^{(k)}\,\mathrm{d}\varsigma \,\mathrm{d}\tau \) | |
5 | 1.5 | \(\int _{0}^{h} \int _{0}^{s}W_{i}(s_{1})\circ \mathrm{d}W_{j}(s_{1}) \circ \mathrm{d}W_{k}(s)\) | \(\int _{0}^{1}z_{\tau}^{(i)}\int _{0}^{1}Z_{\tau ,\xi}^{(j)} \int _{0}^{1}Z_{\xi ,\varsigma}^{(k)}\,\mathrm{d}\varsigma \,\mathrm{d}\xi \,\mathrm{d}\tau \) | |
6 | 1.5 | \(\int _{0}^{h}s\circ \mathrm{d}W_{i}(s)\) | \(\int _{0}^{1}z_{\tau}^{(i)}\int Z_{\tau ,\xi}^{(0)}\,\mathrm{d}\xi \,\mathrm{d}\tau \) | |
7 | 1.5 | \(\int _{0}^{h}W_{i}(s)\,\mathrm{d}s\) | \(\int _{0}^{1}z_{\tau}^{(0)} \int _{0}^{1}Z_{\tau ,\xi}^{(i)}\,\mathrm{d}\xi \,\mathrm{d}\tau \) |