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Some new concentration inequalities for the Itô stochastic integral

Nguyen Tien Dung

Abstract

In this paper, based on the techniques of Malliavin calculus, we provide some new concentration inequalities for the running supremum of the Itô stochastic integral with unbounded integrands. Several applications and examples are provided as well.

Some new concentration inequalities for the Itô stochastic integral

Abstract

In this paper, based on the techniques of Malliavin calculus, we provide some new concentration inequalities for the running supremum of the Itô stochastic integral with unbounded integrands. Several applications and examples are provided as well.
Paper Structure (7 sections, 11 theorems, 95 equations)

This paper contains 7 sections, 11 theorems, 95 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Main results
  4. Applications
  5. Gaussian functionals
  6. Supremum of double Wiener-Itô integrals
  7. Supremum of Cox-Ingersoll-Ross process

Key Result

Lemma 2.1

Let $Z$ be a centered random variable in $\mathbb{D}^{1,2}.$ Assume there exists a non-random constant $M$ such that Then the following estimate for tail probabilities holds:

Theorems & Definitions (25)

  • Lemma 2.1
  • proof
  • Lemma 3.1
  • proof
  • Theorem 3.1
  • proof
  • Remark 3.1
  • Corollary 3.1
  • Corollary 3.2
  • proof
  • ...and 15 more