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Orthogonal intertwiners for infinite particle systems in the continuum

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  • Wagner, Stefan

Abstract

This article focuses on a system of sticky Brownian motions, also known as Howitt–Warren martingale problem, and correlated Brownian motions and shows that infinite-dimensional orthogonal polynomials intertwine the dynamics of infinitely many particles and their n-particle evolution. The proof is based on two assumptions about the model: information about the reversible measures for the n-particle dynamics and consistency. Additionally, explicit formulas for the polynomials are used, including a new explicit formula for infinite-dimensional Meixner polynomials, the orthogonal polynomials with respect to the Pascal process. As an application of the intertwining relations, new reversible measures for the infinite-particle dynamics are obtained.

Suggested Citation

  • Wagner, Stefan, 2024. "Orthogonal intertwiners for infinite particle systems in the continuum," Stochastic Processes and their Applications, Elsevier, vol. 168(C).
    • Handle: RePEc:eee:spapps:v:168:y:2024:i:c:s0304414923002417
    DOI: 10.1016/j.spa.2023.104269
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    References listed on IDEAS

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    4. Brockington, Dom & Warren, Jon, 2023. "The Bethe ansatz for sticky Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 162(C), pages 1-48.
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