On the efficiency of the splitting and roulette approach for sensitivity analysis

The paper is devoted to a brief review of a mathematical theory for the branching variance-reduction technique. The branching technique is an extension of von Neumann's splitting and Russian roulette approach. The efficiency increase is attained by parallel simulation of several independent paths of the random process under consideration, the number of which is regulated by procedures of splitting and roulette. These procedures are governed by a probability measure whose optimal choice is the main problem of the corresponding mathematical theory. The relation between splitting and roulette approach and sensitivity analysis is discussed in the introduction.