Numerical discretisation of stochastic (partial) differential equations
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 10^3 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 methods.