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Once again about weak uniqueness for SDE with singular coefficients

N. V. Krylov

Abstract

We prove weak uniqueness for admissible solutions of Itô's equations with uniformly nondegenerate $a$ which is almost in VMO and $b$ in a Morrey class of functions with low integrability property. If $b\in L_{d}$ any solution is admissible.

Once again about weak uniqueness for SDE with singular coefficients

Abstract

We prove weak uniqueness for admissible solutions of Itô's equations with uniformly nondegenerate which is almost in VMO and in a Morrey class of functions with low integrability property. If any solution is admissible.

Paper Structure

This paper contains 4 sections, 15 theorems, 92 equations.

Table of Contents

  1. Introduction
  2. Parabolic Morrey spaces and main results
  3. Properties of $E_{p,q,\beta}$
  4. Solvability of parabolic equations and weak uniqueness of solutions of (\ref{['11.29.20']})

Key Result

Theorem 2.4

For $\beta<2$ and $p_{b}\geq p\beta$ there exist $\check a=\check a (d,\delta,p,q)>0$ and $\check b=\check b_{0} (d,\delta,p,q,\rho_{a},\beta)>0$ (defined in Section section 3.27.3) such that, if $a^{\# }_{\rho_{a}}\leq \check a$ and $\hat{b}_{\rho_{b}}\leq \check b$, then any two $E_{p,q,\beta}$- o

Theorems & Definitions (32)

  • Remark 1.1
  • Remark 1.2
  • Definition 2.1
  • Remark 2.2
  • Remark 2.3
  • Theorem 2.4: weak uniqueness
  • Remark 2.5
  • Remark 2.6
  • Remark 2.7
  • Example 2.8: see also Example \ref{['example 7,29.1']}
  • ...and 22 more