We study the $gamma$-ray emission from the pulsar magnetosphere based on outer gap models, and the TeV radiation from pulsar wind nebulae (PWNe) through inverse Compton scattering using a one-zone model. We showed previously that GeV radiation from the magnetosphere of mature pulsars with ages of $sim 10^5-10^6$ years old can contribute to the high latitude unidentified EGRET sources. We carry out Monte Carlo simulations of $gamma$-ray pulsars in the Galaxy and the Gould Belt, assuming the pulsar birth rate, initial position, proper motion velocity, period, and magnetic field distribution and evolution based on observational statistics. We select from the simulation a sample of mature pulsars in the Galactic plane ($|b|leq 5^circ$) and in the high latitude ($|b|> 5^circ$) which could be detected by EGRET. The TeV flux from the pulsar wind nebulae of our simulated sample through the inverse Compton scattering by relativistic electrons on the microwave cosmic background and synchrotron seed photons are calculated. The predicted fluxes are consistent with the present observational constraints. We suggest that strong EGRET sources can be potential TeV source candidates for present and future ground-based TeV telescopes.
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