We consider Riemann sum approximations of stochastic integrals with respect to the fractional Browian motion index H≥1 2. show convergence these schemes at first and second order. The processes obtained in limit case are Rosenblatt process if H>3 4 standard Brownian otherwise. These results under assumption that integrand is a “controlled” process. provide many examples such processes, particul...

We consider a model of 2D gravity with the action quadratic in curvature and represent path integrals as over SL(2,R) invariant Gaussian functional measure. reduce these to products Wiener calculate correlation function metric first perturbative order.

We prove that Poisson measures are invariant under (random) intensity preserving transformations whose finite difference gradient satisfies a cyclic vanishing condition. The proof relies on moment identities of independent interest for adapted and anticipating Poisson stochastic integrals, and is inspired by the method of Üstünel and Zakai, Probab. Theory Relat. Fields 103, 1995, on the Wiener ...