We consider N independent stochastic processes (Xj(t),t∈[0,T]), j=1,…,N, defined by a one-dimensional stochastic differential equation with coefficients depending on a random variable ϕj and study the nonparametric estimation of the density of the random effect ϕj in two kinds of mixed...

Consider a compound Poisson process which is discretely observed with sampling interval <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\Delta $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="normal">Δ</mi> </math> </EquationSource> </InlineEquation> until exactly <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$n$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>n</mi> </math> </EquationSource> </InlineEquation> nonzero increments are obtained. The jump density and the intensity of the Poisson process are unknown. In this paper, we build and study parametric estimators...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>