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Malliavin calculus for non-colliding particle systems

Author

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  • Naganuma, Nobuaki
  • Taguchi, Dai

Abstract

In this paper, we use Malliavin calculus to show the existence and continuity of density functions of d-dimensional non-colliding particle systems such as hyperbolic particle systems and Dyson Brownian motion with smooth drift. For this purpose, we apply results proved by Florit and Nualart (1995) and Naganuma (2013) on locally non-degenerate Wiener functionals.

Suggested Citation

  • Naganuma, Nobuaki & Taguchi, Dai, 2020. "Malliavin calculus for non-colliding particle systems," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 2384-2406.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:4:p:2384-2406
    DOI: 10.1016/j.spa.2019.07.005
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    References listed on IDEAS

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    1. Kusuoka, Seiichiro, 2017. "Continuity and Gaussian two-sided bounds of the density functions of the solutions to path-dependent stochastic differential equations via perturbation," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 359-384.
    2. Florit, Carme & Nualart, David, 1995. "A local criterion for smoothness of densities and application to the supremum of the Brownian sheet," Statistics & Probability Letters, Elsevier, vol. 22(1), pages 25-31, January.
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