The stochastic behavior of inter-core crosstalk in multi-core fiber is discussed based on a theoretical model validated by measurements, and the effect of the crosstalk on the Q-factor in transmission systems, using multi-core fiber is investigated theoretically. The measurements show that the crosstalk rapidly changes with wavelength, and gradually changes with time, in obedience to the Gaussian distribution in I-Q planes. Therefore, the behavior of the crosstalk as a noise may depend on the bandwidth of the signal light. If the bandwidth is adequately broad, the crosstalk may behave as a virtual additive white Gaussian noise on I-Q planes, and the Q-penalty at the Q-factor of 9.8dB is less than 1dB when the statistical mean of the crosstalk from other cores is less than -16.7dB for PDM-QPSK, -23.7dB for PDM-16QAM, and -29.9dB for PDM-64QAM. If the bandwidth is adequately narrow, the crosstalk may behave as virtually static coupling that changes very gradually with time and heavily depends on the wavelength. To cope with a static crosstalk much higher than its statistical mean, a margin of several decibels from the mean crosstalk may be necessary for suppressing Q-penalty in the case of adequately narrow bandwidth.