Reduction of the Ito functional integral associated with two-dimensional non-constant diffusion process with drift to the Wiener type path integral

In the present paper we propose a method of reduction the functional integral with respect to the Ito measure for two-dimensional drift-diffusion process with variable coefficients to the functional integral over the Wiener measure. The Ito measure functional integral represents the fundamental solution of the backward Kolmogorov equation corresponding to the above drift-diffusion process. Such reduction allows finally to deal only with Wiener functional integrals for which there is a unique relationship with path integrals which can be either computed or effectively analyzed. The proposed constructions for two-dimensional drift-diffusion processes in general form are applied to the known models of stochastic volatility options and give in this case a number of new results.