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Some identities in law for Bessel processes. (Quelques identités en loi pour les processus de Bessel.) (French) Zbl 0863.60035
Hommage à P. A. Meyer et J. Neveu. Paris: Société Mathématique de France, Astérisque. 236, 249-276 (1996).
\((R_t\), \(t\geq 0)\) is a Bessel process of dimension \(\delta> 0\), starting from \(0\), and \((r(t)\), \(0\leq t\leq 1)\) is a standard Bessel bridge \((r(0)=r(1)=0)\) of dimension \(\delta> 0\). The object is to prove and gather some identities in law relative to \(\int_0^1{ds\over R_s}\), \(\int_0^1 R_s^2ds\), \(\sup_{s\leq 1} R_s\) and the corresponding functionals for \(r\). It is worth to mention that some of these identities are interesting for the calculus of some option’s prices, and also for the estimation of fundamental solutions for nonlinear equations, \(u_t-{1\over 2}\Delta u=-|\nabla u|\) in \(R^d\) \((d\geq 2)\).
For the entire collection see [Zbl 0847.00013].

60G07 General theory of stochastic processes
60H05 Stochastic integrals
60J99 Markov processes