Iterated integrals with respect to Bessel processes

Let X=(Xt)t⩾0 be the square of a δ (⩾0)-dimensional Bessel process starting at zero. Define iterated stochastic integrals In(t,δ), t⩾0 inductively byIn(t,δ)=∫0tIn-1(s,δ)dXswith I0(t,δ)=1 and I1(t,δ)=Xt. Then the inequalitiescn,p,δ∥τn∥p⩽sup0⩽t⩽τ|In(t,δ)|p⩽Cn,p,δ∥τn∥pandcn,p,δ∥Gδ(τ)n∥p⩽sup0⩽t⩽τ|In(t,δ)|/(1+t)np⩽Cn,p,δ∥Gδ(τ)n∥pare proved to hold for all 0