formula

$P(M_t>y)&=& P(R_t^2< r^2)\quad (r=1/y^{1/d-2})\\ &=&\int_{\{x_1^2+\ldots +x_d^2<r^2\}}\frac{1}{(2\pi t)^{d/2}}\exp(-\frac{\sum_{j=1}^dx_j^2}{2t})dx_1\ldots dx_d\\ &\leq&\frac{1}{(2\pi t)^{d/2}}\int_{\{x_1^2+\ldots +x_d^2<r^2\}}dx_1\ldots dx_d\\ &=&\frac{1}{(2\pi t)^{d/2}} \frac{\pi^{d/2}}{\Gamma(d/2+1)}y^{-d/(d-2)}$