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Gaussian structure in coalescing stochastic flows

A. A. Dorogovtsev, E. V. Glinynaya

Abstract

In the paper we consider the point measure that corresponds to Arratia flow. The central limit theorem of the multiple integrals with respect to this measure was obtained.

Gaussian structure in coalescing stochastic flows

Abstract

In the paper we consider the point measure that corresponds to Arratia flow. The central limit theorem of the multiple integrals with respect to this measure was obtained.

Paper Structure

This paper contains 5 sections, 21 theorems, 120 equations.

Table of Contents

  1. Introduction.
  2. Finite-dimensional central limit theorem for $\mathbf{(A_t)_ {t>0}}$
  3. Central limit theorem for conditional expectations.
  4. Convergence of integrals in functional spaces.
  5. Limiting Gaussian process as a functional.

Key Result

Lemma \oldthetheorem

For any symmetric non-negative function $f$ we have where the constants $A_{l_1,\ldots, l_k}^n$ and $a_{l_1,\ldots, l_k}^n$ do not depend on $f$ and $N$

Theorems & Definitions (45)

  • Definition \oldthetheorem
  • Definition \oldthetheorem
  • Lemma \oldthetheorem: DV
  • Theorem \oldthetheorem
  • proof
  • Remark \oldthetheorem
  • Lemma \oldthetheorem
  • Remark \oldthetheorem
  • Theorem \oldthetheorem
  • proof
  • ...and 35 more