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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].

##### MSC:
 60G07 General theory of stochastic processes 60H05 Stochastic integrals 60J99 Markov processes
##### Keywords:
Bessel process; Bessel bridge