Stability of compensator integrals and nonlinear operators under canonical p-th power variation convergence

Let \(X\) and \((X^n)_{n\ge1}\) be c`adl`ag processes with predictable compensators \(ν\) and \(ν^n\). For \(p>1\), assume that \([X^n-X]^{(p)}_t\to0\) in probability, where \([\,\cdot\,]^{(p)}\) denotes canonical \(p\)-th power variation. We prove canonical \(p\)-th power-variation stability for a