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<p>We extend the stochastic reconstruction theorem to a setting in which the underlying family of distributions satisfies natural conditions involving rectangular increments. This allows us to establish the well-posedness of a new class of mixed stochastic partial differential equations of hyperbolic type, which combine standard Walsh stochastic integration with Young products.</p>

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A stochastic reconstruction theorem on rectangular increments with an application to a mixed hyperbolic SPDE

  • 期刊论文

  • 发表日期：

    2025年6月22日

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  • Carlo Bellingeri,
  • Hannes Kern

摘要

We extend the stochastic reconstruction theorem to a setting in which the underlying family of distributions satisfies natural conditions involving rectangular increments. This allows us to establish the well-posedness of a new class of mixed stochastic partial differential equations of hyperbolic type, which combine standard Walsh stochastic integration with Young products.