This paper uses Lie symmetry methods to calculate certain expectations for a large class of Ito diffusions. We show that if the problem has sufficient symmetry, then the problem of computing functionals of the form ...

In this paper we present some new applications of Lie symmetry analysis to problems in stochastic calculus. The major focus is on using Lie symmetries of parabolic PDEs to obtain fundamental solutions and transition ...

We obtain fundamental solutions for PDEs of the form u(t) = sigma x(gamma)u(xx) + f(x)u(x) - mu x(r)u by showing that if the symmetry group of the PDE is nontrivial, it contains a standard integral transform of the fundamental ...

We consider families of linear, parabolic PDEs in n dimensions which possess Lie symmetry groups of dimension at least four. We identify the Lie symmetry groups of these equations with the (2n+1)-dimensional Heisenberg ...