Extended Itô integrals and the reflection problem (Q1288942)

The author suggests a new approach to construct extended Itô path integrals. The class of integrands contains, in particular, all functions which are right-continuous and have finite left limits. This approach has no connection with the classical definition of an integral as the limit of integral sums. Under some conditions the integral coincides with the integral along the Gaussian process and some other processes. The author reveals the connection between the construction of integrals and partial differential equations of parabolic type. Another application is given in the financial mathematics: the author deduces the generalized Black-Scholes equation for the model with variable volatility that depends upon the stock price.