Convergence of U-statistics indexed by a random walk to stochastic integrals of a Levy sheet
Convergence of U-statistics indexed by a random walk to stochastic integrals of a Levy sheet
We establish limit theorems for U-statistics indexed by a random walk on Z^d and we express the limit in terms of some Levy sheet Z(s,t). Under some hypotheses, we prove that the limit process is Z(t,t) if the random walk is transient or null-recurrent ant that it is some stochastic …