# Stochastic differential equations with singular (form-bounded) drift

## TL;DR

This paper addresses the challenge of constructing weak solutions for stochastic differential equations with highly singular drifts and discontinuous dispersion matrices, focusing on critical-order singularities and discontinuities.

## Contribution

It introduces methods for constructing weak solutions to SDEs with critical singularities and discontinuities in drift and dispersion, advancing the understanding of such complex stochastic systems.

## Key findings

- Successfully constructed weak solutions for SDEs with singular drifts
- Extended the theory to include critical-order discontinuities
- Provided new techniques for handling singularities in stochastic equations

## Abstract

We consider the problem of constructing weak solutions to the It\^{o} and to the Stratonovich stochastic differential equations having critical-order singularities in the drift and critical-order discontinuities in the dispersion matrix.