Creating an Apex Test Class for a Custom Object as a Process Object and a Step
To deploy the trigger to your production environment, create the following class.
If your custom object is the detail record in a master–detail relationship, create a formula field that retrieves the OwnerId from the master object. The structure of the field depends on how the relationship is named. For example, if your object is related to the account object through a master–detail relationship, the formula is: Business_Account__r.OwnerId.
Refer to the Deploy from Sandbox with Change Sets module in Trailhead for instructions on the deployment process.