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Distance between closed sets and the solutions to stochastic partial differential equations

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  • Toshiyuki Nakayama
  • Stefan Tappe

Abstract

The goal of this paper is to clarify when the solutions to stochastic partial differential equations stay close to a given subset of the state space for starting points which are close as well. This includes results for deterministic partial differential equations. As an example, we will consider the situation where the subset is a finite dimensional submanifold with boundary. We also discuss applications to mathematical finance, namely the modeling of the evolution of interest rate curves.

Suggested Citation

  • Toshiyuki Nakayama & Stefan Tappe, 2022. "Distance between closed sets and the solutions to stochastic partial differential equations," Papers 2205.00279, arXiv.org, revised Oct 2024.
    • Handle: RePEc:arx:papers:2205.00279
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    5. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
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