Admissibility conditions for a class of quadrature formulas with random nodes

Admissibility of Monte Carlo Procedures

“…Therefore, by virtue of Lemma 2, in studying the admissibility problem we will restrict our consideration to symmetric MCP's € Κ^ χ Vf χ F. The following theorem which characterizes the class of MCP's considered strengthens the corresponding results of [12], [13]. to i=l Thus, we obtain from (8), …”

“…The variance of the considered MCP can be found with the help of (12). In this case Αίχ^ = Ν ^μ(Χ), Note also that the density Ν £ u.…”

“…In the theory of the Monte Carlo method, the concept of admissibility was first introduced by Ermakov [10] and subsequently studied by the author in [12], [13]. The aim of introducing this concept was twofold:…”