Portal de Periódicos da CAPES

Poisson perturbations

1999; EDP Sciences; Volume: 3; Linguagem: Inglês

10.1051/ps

1292-8100

Andrew D. Barbour, Aihua Xia,

Probability and Risk Models

Stein's method is used to prove approximations in total variation to the distributions of integer valued random variables by (possibly signed) compound Poisson measures. For sums of independent random variables, the results obtained are very explicit, and improve upon earlier work of Kruopis (1983) and Čekanavičius (1997); coupling methods are used to derive concrete expressions for the error bounds. An example is given to illustrate the potential for application to sums of dependent random variables.