  Based on a student research project this article gives a short review on
Wishart processes. A Wishart procces is a matrix valued continuous time
stochastic process with a marginal Wishart distribution. The Wishart
distribution is a matrix variate generalization of the chi-squared
distribution. Since Wishart processes are defined as a solution to a stochastic
differential equation, the existence and uniqueness of strong solutions will be
discussed comprehensively. It is also shown that some solutions of the
stochastic differential equation can be expressed as squares of matrix variate
Ornstein-Uhlenbeck processes. Wishart processes have the property of being
symmetric positive definite and are therefore heavily used for modeling
interest rates or the covariance matrix in stochastic volatility models.
