How can we write business logic in vertica

You can write business logic or procedures via Stored Procedures or via User-Defined Extensions (UDxs).
See:
https://www.vertica.com/docs/11.1.x/HTML/Content/Authoring/ExtendingVertica/StoredProcedures/StoredProcedures.htm
https://www.vertica.com/docs/11.1.x/HTML/Content/Authoring/ExtendingVertica/UDx/DevelopingUDxs.htm

Thank you for update, above info useful for me .

I think, this feature is not exist till 10.x version
Might be, this feature came in 11.x version