First hitting place distributions for two-dimensional Wiener processes (Q1580826)

The author studies the distribution of the first hitting place of the process \[ x(t)\doteq x(0)+ \int^t_0\bigl(B^2 (s)+W^2(s)\bigr)ds, \] where \(W\) and \(B\) are independent one-dimensional Brownian motions, the initial value \(x(0)\in \mathbb{R}^2\) is located between two circles \(C_1\) and \(C_2\) and \(\tau\) is the first hitting time to circle \(C_1\) or to circle \(C_2\). The author computes the Laplace transform of \(x(\tau)\) and uses it to compute moments etc. The main result is the same as the formula 4.3.9.1 of \textit{A. N. Borodin} and \textit{P. Salminen} [``Handbook of Brownian motion. Facts and formulae'' (1996; Zbl 0859.60001), p. 308], and a standard Feynman-Kac computation.