<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>

This paper deals with the spectrum of the almost periodically correlated (APC) processes defined on . It is established that the covariance kernel of such a process admits a Fourier series decomposition, K(s+t, s) , whose coefficient functions b[alpha] are the Fourier transforms of complex...

If a positive definite bimeasure, M: - -- C, on any measurable space ([Omega], ) is extendable to a complex measure M', on the product [sigma]-algebra [circle times operator] , one can define its trace M'[Delta] on the diagonal [Delta] of [Omega] - [Omega]. If M is not extendable, the definition...

In order to state sufficient conditions for the harmonizability of the product time series of two harmonizable time series, the notion of Lp-harmonizable time series is introduced for 1 [less-than-or-equals, slant] p [less-than-or-equals, slant] + [infinity]. Then, the problem of the product of...

We prove that every harmonizable process with [sigma]-finite bimeasure is asymptotically stationary and we give its associated spectral measure.