# Distance covariance for stochastic processes

## TL;DR

This paper introduces a new measure of dependence called distance covariance for stochastic processes, enabling tests of independence between processes, extending the concept from finite vectors to infinite-dimensional settings.

## Contribution

It proposes an analog of distance covariance for stochastic processes and develops empirical versions for testing independence between such processes.

## Key findings

- Provides a new dependence measure for stochastic processes.
- Enables statistical testing of independence between processes.
- Extends finite-dimensional dependence concepts to infinite-dimensional processes.

## Abstract

The distance covariance of two random vectors is a measure of their dependence. The empirical distance covariance and correlation can be used as statistical tools for testing whether two random vectors are independent. We propose an analogs of the distance covariance for two stochastic processes defined on some interval. Their empirical analogs can be used to test the independence of two processes.