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Yes it is possible to display custom thank you message after the form is submitted. Please check the screenshot below:
It is also possible to redirect users to you own page after the form is submitted. You should actually set the "Custom URL" (Thank you) of your form. The following guide should help you: https://www.jotform.com/help/38-Redirecting-Users-to-a-Different-Page
You may also like to take a look at the following guide as well: https://www.jotform.com/help/211-Setting-Up-the-Thank-You-Page
Hope this helps.
Do get back to us if you have any questions.