Lattice schemes for an elliptic SPDE with fractional noise
2012-01-10 14:30 2012-01-10 15:30 2012-01-10 14:30 .. 15:30
by Iván Torrecilla Tarantino (Univ. Barcelona / GFMUL)
We consider a stochastic boundary value elliptic problem on a bounded domain D of R^k, driven by a fractional Brownian field with Hurst parameter H =(H^1,...,H^k) in [1/2, 1[^k. First, we define the stochastic convolution derived from the Green kernel and prove some properties. Using monotonicity methods, we prove existence and uniqueness of solution along with regularity of the sample paths.
Finally, we propose a sequence of lattice approximations and prove its convergence to the solution of the SPDE at a given rate.