# Random dynamical systems generated by coalescing stochastic flows on $\mathbb{R}$

## TL;DR

This paper proves the existence of random dynamical systems for coalescing stochastic flows on the real line, introduces a new state space, and examines specific cases like solutions to stochastic differential equations and Harris flows.

## Contribution

It establishes a framework for random dynamical systems generated by coalescing flows and constructs a novel state space for their analysis.

## Key findings

- Existence of random dynamical systems for coalescing flows on R.
- Construction of a new state space for coalescing flows.
- Application to stochastic differential equations and Harris flows.

## Abstract

Existence of random dynamical systems for a class of coalescing stochastic flows on $\mathbb{R}$ is proved. A new state space for coalescing flows is built. As particular cases coalescing flows of solutions to stochastic differential equations independent before meeting time and coalescing Harris flows are considered.