I am interested in the numerical discretisation of
stochastic (partial) differential equations (SPDEs).
To test the convergence, or other properties,
of the numerical solutions, one often has
to compute the expectations of some
quantities. One thus need to simulate
many many times the solution of such
a stochastic problem. In the SPDE
context, one thus has to solve M times
a partial differential equation, where M should be
of the order of 10^6 or more, in order
to have M samples of the numerical solutions.
Once this is done, one can use this information
to approximate the above expectations and
thus confirm the good behaviour of the numerical
Thank you for your understanding.