Stochastic search algorithm with an application to multidimensional integration
Konstantin Aleksandrovich Borovkov · Annales Academiae Scientiarum Fennicae Series A I Mathematica · 1992
Recently Lalley and Robbins [2] suggested an asymptotically minimax strategy of stochastic search for the so-called "princess and monster" game.According to this strategy, the movement of the monster in a convex domain O on the plane, while it is looking for the princess, can be described by a piecewise linear ergodic semi-Markov process X(t), whose stationary distribution proves to be uniform on O. Thus, for any integrablefunction / on O one has lim 1l ---+ oo r -I.:1," f(x(r)) d,t-* -m ä's'' f (*) p(d*) ,