On orthogonally exponential functionals

On Some Exponential Functionals of Brownian Motion

In this paper, distributional questions which arise in certain Mathematical Finance models are studied: the distribution of the integral over a fixed time interval {0, T} of the exponential of Brownian motion with drift is computed explicitly, with the help of former computations made by the author for Bessel processes. The moments of this integral are obtained independently and take a particul...

On exponential functionals of Lévy processes

Exponential functionals of Lévy processes appear as stationary distributions of generalized Ornstein-Uhlenbeck (GOU) processes. In this paper we obtain the infinitesimal generator of the GOU process and show that it is a Feller process. Further we use these results to investigate properties of the mapping Φ, which maps two independent Lévy processes to their corresponding exponential functional...

Exponential Functionals of Lévy Processes

This text surveys properties and applications of the exponential functional R t 0 exp(−ξs)ds of real-valued Lévy processes ξ = (ξt, t ≥ 0).

Aimd Algorithms and Exponential Functionals

ABSTRACT. The behavior of connection transmitting packets into a network according to a general additive-increase multiplicative-decrease (AIMD) algorithm is investigated. It is assumed that loss of packets occurs in clumps. When a packet is lost, a certain number of subsequent packets are also lost (correlated losses). The stationary behavior of this algorithm is analyzed when the rate of occu...

Further Results on Exponential Functionals of Brownian Motion