Before revision: We study the valuation partial differential equation for European contingent claims in a general framework of stochastic volatility models . The standard Feynman-Kac theorem cannot be directly applied because the diffusion coefficients may  degenerate on the boundaries of the state space and grow faster than linearly .
After revision: We study the valuation partial differential equation for European contingent claims in a general framework of stochastic volatility models where the standard Feynman-Kac theorem cannot be directly applied because the diffusion coefficients may degenerate on the boundaries of the state space and grow faster than linearly .