<Para ID="Par1">We study the asymptotic behavior of the weighted least squares estimators of the unknown parameters of bifurcating integer-valued autoregressive processes. Under suitable assumptions on the immigration, we establish the almost sure convergence of our estimators, together with a quadratic strong...</para>

<Para ID="Par1">In this paper we investigate the large-sample behaviour of the maximum likelihood estimate (MLE) of the unknown parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\theta $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="italic">θ</mi> </math> </EquationSource> </InlineEquation> for processes following the model <Equation ID="Equ38"> <EquationSource Format="TEX">$$\begin{aligned} d\xi _{t}=\theta f(t)\xi _{t}\,dt+d\mathrm {B}_t, \end{aligned}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink" display="block"> <mrow> <mtable columnspacing="0.5ex"> <mtr> <mtd columnalign="right"> <mrow> <mi>d</mi> <msub> <mi mathvariant="italic">ξ</mi> <mi>t</mi> </msub> <mo>=</mo> <mi mathvariant="italic">θ</mi> <mi>f</mi> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <msub> <mi mathvariant="italic">ξ</mi>...</msub></mrow></mtd></mtr></mtable></mrow></math></equationsource></equationsource></equation></equationsource></equationsource></inlineequation></para>

We discuss some inference problems associated with the fractional Ornstein–Uhlenbeck (fO–U) process driven by the fractional Brownian motion (fBm). In particular, we are concerned with the estimation of the drift parameter, assuming that the Hurst parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$H$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>H</mi> </math> </EquationSource> </InlineEquation> is known and is in <InlineEquation ID="IEq2"> <EquationSource...</equationsource></inlineequation></equationsource></equationsource></inlineequation>