, Volume 17, Issue 3, pp 693-703

Small Ball Asymptotics for the Stochastic Wave Equation

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Abstract

We examine the small ball asymptotics for the weak solution X of the stochastic wave equation $$\frac{{\partial ^2 X}}{{\partial t^2 }}(t,x) - \frac{{\partial ^2 X}}{{\partial x^2 }}(t,x) = g(X(t,x)) + f(t,x)dW(t,x)$$ on the real line with deterministic initial conditions.