Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Stratonovich-type integral with respect to a general stochastic measure

Vadym Radchenko

Abstract

Let $μ$ be a general stochastic measure, where we assume for $μ$ only $σ$-additivity in probability and continuity of paths. We prove that the symmetric integral $\int_{[0,T]}f(μ_t, t)\circ\,{\rm d}μ_t$ is well defined. For stochastic equations with this integral, we obtain the existence and uniqueness of a solution.

Stratonovich-type integral with respect to a general stochastic measure

Abstract

Let be a general stochastic measure, where we assume for only -additivity in probability and continuity of paths. We prove that the symmetric integral is well defined. For stochastic equations with this integral, we obtain the existence and uniqueness of a solution.

Paper Structure

This paper contains 6 sections, 10 theorems, 56 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. SM has finite strong cubic variation
  4. Stratonovich-type integral
  5. SDE driven by SM
  6. Some counterexamples

Key Result

Theorem 2.1

dretop Let $\mu_n$ are SMs on ${\mathcal{B}}$, $n\ge 1$, and Then $\mu$ is a SM on ${\mathcal{B}}$.

Theorems & Definitions (21)

  • Definition 2.1
  • Theorem 2.1
  • Lemma 3.1
  • Corollary 3.1
  • proof
  • Theorem 3.1
  • proof
  • Corollary 3.2
  • Lemma 4.1
  • Corollary 4.1
  • ...and 11 more