Asymptotically homogeneous iterated random functions with applications to the HARCH processLithuanian Mathematical Journal - Tập 49 - Trang 26-39 - 2009
V. Kazakevičius, V. Skorniakov
We show that a certain class of Markov chains satisfies the general Foster–Lyapunov condition under nonrestrictive assumptions. In particular, if a chain belongs to this class, the existence of an invariant measure can be established by means of the theorem provided. As an application of the theorem, the HARCH process is considered.
Compound Poisson Approximations to Sums of Extrema of Bernoulli VariablesLithuanian Mathematical Journal - Tập 62 - Trang 481-499 - 2022
Gabija Liaudanskaite, Vydas Čekanavičius
Let Sn = X1 + X2 + · · · + Xn, where Xj = max(ξj, ξj+1), and ξ1, ξ2, . . . , ξn+1 are independent Bernoulli random variables. If all P(ξj = 1) are small, then we approximate Sn by a compound Poisson random variable with two matching moments. If all P(ξj = 1) are large, then we apply compound Poisson and negative binomial approximations to n − Sn. We estimate the accuracy of approximation in the to...... hiện toàn bộ