Conclusion

• When used with care, Monte Carlo methods can be used to solve problems that are otherwise intractible.

• The choice of the random number generator must be carefully considered.
  • The built in generator in your compiler library should not be used for serious applications
  • There is no universal, single best generator.
  • For some problems quasi-random numbers provide more accurate results than pseudo-random numbers.

• For the estimation of definite integrals in high dimension (above about 5), a Monte Carlo method using Quasi-random is the best approach to use.

• Markov chains can be used for solving some very difficult problems.