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Extrinsic Derivative Formula for Distribution Dependent SDEs

Panpan Ren

Abstract

A Bismut type formula is established for the extrinsic derivative of distribution dependent SDEs. The main result is illustrated by nondegenerate DDSDEs with space time singular drift, as well as degenerate DDSDEs with weakly monotone coefficients.

Extrinsic Derivative Formula for Distribution Dependent SDEs

Abstract

A Bismut type formula is established for the extrinsic derivative of distribution dependent SDEs. The main result is illustrated by nondegenerate DDSDEs with space time singular drift, as well as degenerate DDSDEs with weakly monotone coefficients.
Paper Structure (7 sections, 6 theorems, 89 equations)

This paper contains 7 sections, 6 theorems, 89 equations.

Table of Contents

  1. Introduction
  2. Remark 1.1.
  3. Lemmas
  4. Proof of Theorem \ref{['T1']}
  5. Two specific models
  6. Singular case
  7. Degenerate case

Key Result

Theorem 1.1

Assume (H). Then the DDSDE E0 is well-posed for distributions in $\mathscr P_k$, and the following assertions hold.

Theorems & Definitions (13)

  • Definition 1.1
  • Theorem 1.1
  • Lemma 2.1
  • proof
  • Lemma 2.2
  • proof
  • Lemma 2.3
  • proof
  • proof : Proof of Theorem \ref{['T1']}(1)
  • proof : Proof of Theorem \ref{['T1']}(2)
  • ...and 3 more