Elliptic self-similar stochastic processes (Q1884103)

Let \(M\) be a random measure and let \(L\) be an elliptic psuedo-differential operator on the \(d\)-dimensional space. The authors study the solution of the stochastic problem \(LX=M\), \(X(0)=0\), when some homogeneity and integrability conditions are assumed. The authors characterize the solutions \(X\) which are self-similar and with stationary increments in terms of the deriving measure \(M\). Then they use appropriate wavelet bases to expand these solutions and give regularity results.