Using motion capture data has nowadays utterly been adopted by video game creators or virtual reality applications. In a context of interactive applications, adapting those data to new situations or producing variants of those motions are known as non trivial tasks. We propose an original method that produces motions that preserve the statistical properties of a reference motion while ensuring some constraints. This method uses principles of conditional stochastic simulation to achieve this goal. Notably, a new real time algorithm, performing sequentially and producing the desired motion is introduced. Possible applications of our method are numerous and several examples are given, along with results.