a Department of Mathematics, University of British Columbia, Vancouver, BC, Canada V6T 1Z2 b Mathematics Department, 110 Frelinghuysen, Rutgers University, Piscataway, NJ 08854, USA
Abstract:
We extend and solve the classical Kolmogorov problem of finding general classes of Kolmogorov equations that can be transformed to the backward heat equation. These new classes include Kolmogorov equations with time-independent and time-dependent coefficients. Our main idea is to include nonlocal transformations. We describe a step-by-step algorithm for determining such transformations. We also show how all previously known results arise as particular cases in this wider framework.