In this paper we study the Bessel process R (μ) t with index μ = 0 starting from x > 0 and killed when it reaches a positive level a, where x > a > 0. We provide sharp estimates of the transition probability density p (μ) a (t, x, y) for the whole range of space parameters x, y > a and every t > 0.
Abstract. In the paper we consider the Bessel differential operator L (µ) = d 2 dx 2 + 2µ + 1 x d dx in half-line (a, ∞), a > 0, and its Dirichlet heat kernel p (µ) a (t, x, y). For µ = 0, by combining analytical and probabilistic methods, we provide sharp two-sided estimates of the heat kernel for the whole range of the space parameters x, y > a and every t > 0, which complements the recent results given in [1], where the case µ = 0 was considered.
Abstract. The main objective of the work is to provide sharp two-sided estimates of λ-Green function of hyperbolic Brownian motion of a half-space. We strongly rely on recent results obtained by K. Bogus and J. Malecki [3], regarding precise estimates of the Bessel heat kernel of half-lines.
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