On ill-posedness of nonlinear stochastic wave equations driven by rough noise

Aurélien Deya

Stochastic Processes and their Applications, 2022, vol. 150, issue C, 215-249

Abstract: We highlight a fundamental ill-posedness issue for nonlinear stochastic wave equations driven by a fractional noise. Namely, if the noise becomes too rough (i.e., the sum of its Hurst indexes becomes too small), then there is essentially no hope to provide a systematic interpretation of the model, whether directly or through a Wick-type renormalization procedure. This phenomenon can be compared with the situation of a general SDE driven by a two-dimensional fractional noise of index H≤14.

Keywords: Nonlinear stochastic wave equation; Fractional noise; Ill-posedness issue (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2022.04.015

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