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A local criterion for smoothness of densities and application to the supremum of the Brownian sheet

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  • Florit, Carme
  • Nualart, David

Abstract

In this note we prove a criterion for the smoothness of the density for a random variable taking values in some open subset of d, and being once differentiable. As an application we show that the maximum of the Brownian sheet on a rectangle [O, s] x [O, t] possesses an infinitely differentiable density.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:22:y:1995:i:1:p:25-31
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    Citations

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    Cited by:

    1. Tomonori Nakatsu, 2019. "Some Properties of Density Functions on Maxima of Solutions to One-Dimensional Stochastic Differential Equations," Journal of Theoretical Probability, Springer, vol. 32(4), pages 1746-1779, December.
    2. Csáki, Endre & Khoshnevisan, Davar & Shi, Zhan, 2000. "Boundary crossings and the distribution function of the maximum of Brownian sheet," Stochastic Processes and their Applications, Elsevier, vol. 90(1), pages 1-18, November.
    3. Nakatsu, Tomonori, 2023. "On density functions related to discrete time maximum of some one-dimensional diffusion processes," Applied Mathematics and Computation, Elsevier, vol. 441(C).
    4. Naganuma, Nobuaki & Taguchi, Dai, 2020. "Malliavin calculus for non-colliding particle systems," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 2384-2406.

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