Yuu Hariya

A pathwise interpretation of the Gorin-Shkolnikov identity

In a recent paper by Gorin and Shkolnikov (2016), they have found, as a corollary to their result relevant to random matrix theory, that the area below a normalized Brownian excursion minus one half of the integral of the square of its total local time, is identical in law with a centered Gaussian random variable with variance

A connection of the Brascamp-Lieb inequality with Skorokhod embedding

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On divergence of expectations of the Feynman-Kac type with singular potentials

. In this note, we give a pathwise interpretation to their identity; Jeulins identity connecting normalized Brownian excursion and its local time plays an essential role in the exposition.

Integration by parts formulae for Wiener measures restricted to subsets in R^d

We reveal a connection of the Brascamp-Lieb inequality with Skorokhod embedding. Error bounds for the inequality in terms of the variance are also provided.

Limiting distributions associated with moments of exponential Brownian functionals

Motivated by the work of Baras-Goldstein (1984), we discuss when expectations of the Feynman-Kac type with singular potentials are divergent. Underlying processes are Brownian motion and

Wiener integrals for centered powers of Bessel processes, I

alpha

Wiener integrals for centered Bessel and related processes, II

-stable process. In connection with the work of Ishige-Ishiwata (2012) concerned with the heat equation in the half-space with a singular potential on the boundary, we also discuss the same problem in the half-space for the case of Brownian motion.