On existence of strong solutions to stochastic equations with Lévy noise and differentiability with respect to initial condition

is a finite sum and always exists. So there will be no other restrictions on b2 (moreover, the general case reduces to that of b2 = 0), but the conditions on other coefficients are important and will be given below. If the coefficients in equation (1.1) are sufficiently regular, then it is known that there exists a unique strong solution to this equation. The goal of this paper is to prove an existence and uniqueness theorem in case where the drift coefficient a can be discontinuous. We shall also prove the differentiability in Lp of the solution φt(x) with respect to the initial condition x. The problem of existence and uniqueness of a strong solutions is well studied in the case where the diffusion coefficient σ is non-degenerate. For example, if