time. Thus, let exp ([[spi:math]]) be the probability that a time interval of length At is free of REP events. The radiation intensity grows from zero in accordance with (51) after each REP event, and so never quite reaches [[spi:math]]. A careful implementation of this model shows that the instantaneous probability for I to be in excess of some arbitrary threshold I0 < [[spi:math]] at any given time is [[spi:math]] (52) The probability that the immediately past interval of duration t0 has been free of REP events is [[spi:math]]. Thus, the probability that I instantaneously exceeds I0 is also exp ([[spi:math]]). It follows from this consideration, and from (54), that 54 and that [[spi:math]]. 00 Here is a simple proof of (52): If t is the elapsed time following the most recent REP event, then it follows from (51) that [[spi:math]] (53) This is the solution of (51) for I(0) = 0. The intensity I0 would thus be attained at time t0, where [[spi:math]] (54) [[spi:math]] [[spi:math]] , (55)
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