Adaptive ISDE based algorithm for the generation of non gaussian vector valued random fields
We address the construction of a random generator for non Gaussian vector valued random fields with values in some arbitrary bounded or emi bounded subsets of the Euclidean space of dimension n. Such an issue typically arises in uncertainty quanti cation for complex systems and multiscale analysis, where the elliptic operators involve stochastic coe cients that may be identi ed by solving statistical inverse problems. The approach builts up on two main features. The first one is the construction of a family of auxiliary random fields converging, in some stochastic sense and at a user controlled rate, towards the target random field. Each of these additional random fi elds is subsequently simulated by solving a family of Ito stochastic diff erential equations. The second aspect is the defi nition of an adaptive algorithm such that the integration step is refi ned on the fly whenever the particle reaches the neighboorhood of the admissible space. A few examples (including comparisons with reference generators) are nally provided so as to illustrate both the adaptivity and the convergence of the solutions.