The process of stratified cross validation involves the following steps: 1. Divide the dataset into k folds, ensuring each fold has the same class distribution as the original dataset. 2. Train the model on k-1 folds and validate it on the remaining fold. 3. Repeat this process k times, each time using a different fold as the validation set. 4. Aggregate the performance metrics from all k iterations to obtain a more reliable estimate of model performance.