  A stochastic model for the energy of a flaring solar active region is
presented, generalising and extending the approach of Wheatland & Glukhov
(1998). The probability distribution for the free energy of an active region is
described by the solution to a master equation involving deterministic energy
input and random jump transitions downwards in energy (solar flares). It is
shown how two observable distributions, the flare frequency-energy distribution
and the flare waiting-time distribution, may be derived from the steady-state
solution to the master equation, for given choices for the energy input and for
the rates of flare transitions. An efficient method of numerical solution of
the steady-state master equation is presented. Solutions appropriate for
flaring, involving a constant rate of energy input and power-law distributed
jump transition rates, are numerically investigated. The flare-like solutions
exhibit power-law flare frequency-energy distributions below a high energy
rollover, set by the largest energy the active region is likely to have. The
solutions also exhibit approximately exponential (i.e. Poisson) waiting-time
distributions, despite the rate of flaring depending on the free energy of the
system.
