# Growth rate of the state vector in a generalized linear stochastic system with symmetric matrix

## TL;DR

This paper analyzes the mean growth rate of the state vector in a generalized linear stochastic second-order system with a symmetric matrix, where diagonal entries are independent exponential variables.

## Contribution

It provides a novel evaluation of the mean growth rate for a specific class of stochastic systems with symmetric matrices and exponential diagonal entries.

## Key findings

- Mean growth rate derived for the system
- Analytical expressions obtained under specified assumptions
- Insights into the impact of matrix entries on system growth

## Abstract

The mean growth rate of the state vector is evaluated for a generalized linear stochastic second-order system with a symmetric matrix. Diagonal entries of the matrix are assumed to be independent and exponentially distributed with different means, while the off-diagonal entries are equal to zero.