Real options with a double continuation region

If the average risk-adjusted growth rate of the project's present value V overcomes the discount rate but is dominated by the average risk-adjusted growth rate of the cost I of entering the project, a non-standard double continuation region can arise: The firm waits to invest in the project if V is insufficiently above I as well as if V is comfortably above I. Under a framework with diffusive uncertainty, we give exact characterization to the value of the option to invest, to the structure of the double continuation region, and to the subset of the primitives'values that support such a region.