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The time-evolution of an excitable reaction-diffusion system of the Bonhoffer-van der Pol type equation is investigated by adding an external noise term. In some parameter regime where the system is monostable, the excited domains can spontaneously nucleate and grow at the expense of the uniform metastable rest state. We formulate a statistical theory of nucleation for this non-variational system where no Lyapunov functional exists. The nucleation rate is calculated approximately as a functiondoi:10.1143/ptps.99.425 fatcat:wibg7ktlfvbttoahhkdlbdwc4e