Non-symmetric hitting distributions on the hyperbolic half-plane and subordinated perpetuities (Q698303)

Summary: We study the law of functionals whose prototype is \(\int^{+\infty}_0e^{B^{(\nu)}_s} dW_s^{\mu}\), where \(B^{(\nu)}\), \(W^{(\mu)}\) are independent Brownian motions with drift. These functionals appear naturally in risk theory as well as in the study of invariant diffusions on the hyperbolic half-plane. Emphasis is put on the fact that the results are obtained in two independent, very different fashions (invariant diffusions on the hyperbolic half-plane and Bessel processes).