There is a statement as follow:
$E(|X_1(t)-X_2(t)|)\leq\int_0^t \kappa[E(|X_1(t)-X_2(t)|)]ds$, where $\kappa$ is a strictly increasing concave function such that $\kappa(0)=0$ and $\int_{0+}\kappa^{-1}(u)du=+\infty$. This can be proved that $E(|X_1(t)-X_2(t)|)=0$.
How can I make the conclusion? I suspect to use Gronwall Inequality but I do not find the one similar to this.
The statement appears on p.184 of Stochastic differential equations and diffusion processes by Ikeda and Watanabe. $X_i(t)$ should be one dimensional process.