Same jsessionid for MyProject.com and param.MyProject.com

Question

Is it possible to keep the same jsessionid on 2 differents url in the same domain?

Example :

I'm on the home page of my site (http://MyProject.com). When I click on a button, I'm redirected to "http://param.MyProject.com". At the moment, the browser doesn't send the current jsessionid and the server creates a new one but I would like to keep the same. The consequence is that when the url changes from MyProject.com to param.MyProject.com, I loose my HttpSession and I'm logged out.

I use tomcat 7 and Chrome or Firefox.

Thanks for your answers.