Positive invariant fields of the nonlinear multiplicative stochastic heat equation in weak disorder are in one-to-one correspondence with bounded positive harmonic functions, inheriting the Martin boundary structure.
Additive-multiplicative stochastic heat equa- tions, stationary solutions, and Cauchy statistics
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Martin Boundary and the Nonlinear Multiplicative Stochastic Heat Equation in Weak Disorder
Positive invariant fields of the nonlinear multiplicative stochastic heat equation in weak disorder are in one-to-one correspondence with bounded positive harmonic functions, inheriting the Martin boundary structure.