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This paper presents a long-term object tracking framework with a moving event camera under general tracking conditions. A first of its kind for these revolutionary cameras, the tracking framework uses a discriminative representation for the object with online learning, and detects and re-tracks the object when it comes back into the field-of-view. One of the key novelties is the use of an event-based local sliding window technique that tracks reliably in scenes with cluttered and textured background. In addition, Bayesian bootstrapping is used to assist real-time processing and boost the discriminative power of the object representation. On the other hand, when the object re-enters the field-of-view of the camera, a data-driven, global sliding window detector locates the object for subsequent tracking. Extensive experiments demonstrate the ability of the proposed framework to track and detect arbitrary objects of various shapes and sizes, including dynamic objects such as a human. This is a significant improvement compared to earlier works that simply track objects as long as they are visible under simpler background settings. Using the ground truth locations for five different objects under three motion settings, namely translation, rotation and 6-DOF, quantitative measurement is reported for the event-based tracking framework with critical insights on various performance issues. Finally, real-time implementation in C++ highlights tracking ability under scale, rotation, view-point and occlusion scenarios in a lab setting.