Estimates on moments of the solutions to stochastic differential equations with respect to martingales in the plane

AbstractLet M = {Mz, z ϵ R2+} be a two-parameter strong martingale, A be a two-parameter increasing process on R2+ = [0, + ∞) × [0, + ∞). Consider the following stochastic differential equations in the plane: Xz = X0 + ∞Rz a(ξ,X)dMξ + ∞Rz b(ξ,X)dAξ for z ϵ R2+. Under some assumptions on the coefficients a, b and the integrators M, A, we prove the existence and uniqueness of solutions for the equations, and obtain some estimates on moments of solution