The continuum directed polymer in L\'evy Noise
Abstract
We present in this paper the construction of a continuum directed polymer model in an environment given by space-time L\'evy noise. One of the main objectives of this construction is to describe the scaling limit of discrete directed polymer in an heavy-tail environment and for this reason we put special emphasis on the case of α-stable noises with α ∈ (1,2). Our construction can be performed in arbitrary dimension, provided that the L\'evy measure satisfies specific (and dimension dependent) conditions. We also discuss a few basic properties of the continuum polymer and the relation between this model and the Stochastic Heat Equation with multiplicative L\'evy noise.
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