1. An apparatus for computing multiple integral of a multidimensional integrand function A to be integrated with using a vector map f with unbounded support which converts an m (m&gE;1) -dimensional vector having real number components into an m-dimensional vector having real number components, by which a multidimensional density function &rgr; for the limiting distribution resulting from repeatedly applying the map f to an m-dimensional vector u is analytically solvable, said apparatus comprising: a first storage unit which stores an m-dimensional vector x&equals;(x 1, x 2,... x m ); a second storage unit which stores a scalar value w; a first computing unit which computes a vector x′&equals;f(x)&equals;(x′ 1, x′ 2,..., x′ m ) resulting from applying said vector map f to said vector x being stored in said first storage unit; a second computing unit which computes a scalar value w′&equals;A(x)/&rgr;(x) based on said vector x being stored in said first storage unit and said scalar value w being stored in said second storage unit; an update unit which updates the value stored in said first storage unit by storing said vector x′ computed by said first computing unit on said first storage unit, and updates the value in said second storage unit by adding said scalar value w′ computed by said second computing unit to a value to be stored in said second storage unit; and an output unit which computes a scalar value s&equals;w/(c&plus;1) based on said scalar value w being stored in said second storage unit when the number of update times by said update unit becomes c (c&gE;1), and outputs said scalar value s as a result of the multiple integral.