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Brownian Motion with a Singular Drift

Dante DeBlassie, Adina Oprisan, Robert G. Smits

Abstract

We study the effect of a power law drift on Brownian motion in the positive half-line, where the order of the drift at 0 and infinity is different.

Brownian Motion with a Singular Drift

Abstract

We study the effect of a power law drift on Brownian motion in the positive half-line, where the order of the drift at 0 and infinity is different.
Paper Structure (7 sections, 28 theorems, 177 equations)

This paper contains 7 sections, 28 theorems, 177 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Lower Bound
  4. Upper Bound: A Special $C^3$ Case
  5. Transformation of Drift
  6. Upper Bound
  7. Proof of Theorem \ref{['thm1.2']}

Key Result

Theorem 1.1

Under the condition eq1.2, the solution $X_t$ of eq1.1 satisfies where

Theorems & Definitions (46)

  • Theorem 1.1
  • Theorem 1.2
  • Lemma 2.1
  • Lemma 2.2
  • proof
  • Lemma 2.3
  • proof
  • Lemma 2.4
  • proof
  • Lemma 2.5
  • ...and 36 more