A universality class in Markovian persistence

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Abstract: We consider the class of Markovian processes defined by the equation

. Such processes are encountered in systems (like coalescing systems) where dynamics creates discrete upward jumps at random instants

t_{k}

and of random height

z_{k}

. We observe that the probability for these processes to remain above their mean value during an interval of time

T

decays as

e x p - h e t a T

defining

h e t a

as the persistence exponent. We show that

h e t a

takes the value

which thereby extends the well known result of the Gaussian noise case to a much larger class of non-Gaussian processes.

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