| Abstract: |
| We consider Markovian stochastic differential equations with low-regular coefficients and their
perturbations by adding a measurable bounded path-dependent drift term. When we assume the diffusion coefficient matrix is uniformly positive definite, then the solution to the perturbed equation is given by the Girsanov transformation of the original equation. By using the expression we obtain the Gaussian two-sided bounds and the continuity of the density function of the solution to the perturbed equation. The perturbation here is a stochastic analogue to the perturbation in the operator analysis. |
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