We consider a process (X (Î±) t )tâˆˆ[0,T ) given by the SDE dX (Î±) t = Î±b(t)X (Î±) t dt+Ïƒ(t) dBt, t âˆˆ [0, T ), with initial condition X 0 = 0, where T âˆˆ (0,âˆž], Î± âˆˆ R, (Bt)tâˆˆ[0,T ) is a standard Wienerâ€¦ (More)

First we consider a process (X (Î±) t )tâˆˆ[0,T ) given by a SDE dX (Î±) t = Î±b(t)X (Î±) t dt + Ïƒ(t) dBt, t âˆˆ [0, T ), with a parameter Î± âˆˆ R, where T âˆˆ (0,âˆž] and (Bt)tâˆˆ[0,T ) is a standard Wienerâ€¦ (More)

We consider th e problem of estim ating an unknown param eter m in case one observes in an interval (rectangle) stationary and nonstationary OrnsteinUhlenbeek processes (sheets), which are shifted byâ€¦ (More)

Suitable normalization of time{homogeneous rotation{invariant random walks on unit spheres S d R d+1 for d > 2 leads to a central limit theorem with a Gaussian limit measure. This paper is devoted toâ€¦ (More)

Dilatively stable processes generalize the class of infinitely divisible self-similar processes. We reformulate and extend the definition of dilative stability introduced by IglÃ³i (2008) usingâ€¦ (More)

A sequence of firstâ€“order integerâ€“valued autoregressive type (INAR(1)) processes is investigated, where the autoregressive type coefficients converge to 1. It is shown that the limiting distributionâ€¦ (More)

The firstâ€“order integerâ€“valued autoregressive (INAR(1)) process is investigated, where the autoregressive coefficient is close to one. It is shown that the limiting distribution of the conditionalâ€¦ (More)

In this paper the integer-valued autoregressive model of order one, contaminated with additive or innovational outliers is studied in some detail, parameter estimation is also addressed. Inâ€¦ (More)

`=1 âˆ« |x|>Îµ |x| Î¼n`(dx) = 0 for all Îµ > 0, where x 7â†’ |x| denotes a fixed homogeneous norm on the Heisenberg group. Professor E. Siebert suggested a way to prove similar results for a Lie group G.â€¦ (More)