Harmonic functions, defined as twice continuously differentiable functions satisfying Laplace’s equation, have long been a subject of intense study in both pure and applied mathematics.

This is a preview. Log in through your library . Abstract The nonlinear second order differential equation satisfied by the homogeneous function y = [ aum + mbujv n + cvm ]k/m, m = j + n, is obtained.

Given a multi-dimensional Itô process whose drift and diffusion terms are adapted processes, we construct a weak solution to a stochastic differential equation that matches the distribution of the Itô ...