  The big jump principle explains the emergence of extreme events for physical
quantities modelled by a sum of independent and identically distributed random
variables which are heavy-tailed. Extreme events are large values of the sum
and they are solely dominated by the largest summand called the big jump.
Recently, the principle was introduced into physical sciences where systems
usually exhibit correlations. Here, we study the principle for a random walk
with correlated increments. Examples are the autoregressive model of first
order and the discretized Ornstein-Uhlenbeck process both with heavy-tailed
noise. The correlation leads to the dependence of large values of the sum not
only on the big jump but also on the following increments. We describe this
behaviour by two big jump principles, namely unconditioned and conditioned on
the step number when the big jump occurs. The unconditional big jump principle
is described by a correlation dependent shift between the sum and maximum
distribution tails. For the conditional big jump principle, the shift depends
also on the step number of the big jump.
