According to the JAX-RS specification, every implementation (like Jersey) must support the per-request behaviour:
3.1.1 Lifecycle and Environment
By default a new resource class instance is created for each request to that resource. First the constructor (see Section 3.1.2) is called, then any requested dependencies are injected (see Section 3.2), then the appropriate method (see Section 3.3) is invoked and finally the object is made available for garbage collection.
An implementation MAY offer other resource class lifecycles, mechanisms for specifying these are outside the scope of this specification. E.g. an implementation based on an inversion-of-control framework may support all of the lifecycle options provided by that framework.
This means if your Resource class is not additionally annotated, it is per-request. One well-known exception are the Spring beans: if your Rest Resource is also a Spring Bean, then Spring specifies the lifecycle of that class. The same about the EJBs (@Singleton)