15 citations · 26 across the 12 of their papers we have counts for
6 papers · 1 filter
On Maximum Increase and Decrease of Brownian Motion
Paavo Salminen, Pierre Vallois
The joint distribution of maximum increase and decrease for Brownian motion up to an independent exponential time is computed. This is achieved by decomposing the Brownian path at…
Limiting laws for long Brownian Bridges perturbed by their one-sided maximum, III
Bernard Roynette, Pierre Vallois, Marc Yor
Results of penalization of a one-dimensional Brownian motion , by its one-sided maximum $\dis (S_t=\sup_{0 \leq u \leq t}X_u)$, which were recently obtained by the authors…
Limiting laws associated with Brownian motion perturbed by its maximum, minmum and local time II
Bernard Roynette, Pierre Vallois, Marc Yor
We obtain probability measures on the canonical space penalizing the Wiener measure by a function of its maximum (resp. minimum, local time). We study the law of the canonical proc…
Limiting laws associated with Brownian motion perturbated by normalized exponential weights I
Bernard Roynette, Pierre Vallois, Marc Yor
We determine the rate of decay of the expectation Z(t) of some multiplicative functional related to Brownian motion up to time t. This permits to prove that the Wiener measure, pen…
Levy processes: Hitting time, overshoot and undershoot II - Asymptotic behaviour
Bernard Roynette, Pierre Vallois, Agnes Volpi
Let (X_t, t>=0) be a Levy process started at 0, with Levy measure nu and T_x the first hitting time of level x>0: T_x:=inf{t>=0; X_t>x}. Let $F(theta, mu, rho,.) be the joint Lapla…
Levy Processes: Hitting time, overshoot and undershoot - part I: Functional equations
Bernard Roynette, Pierre Vallois, Agnes Volpi
Let (X_t, t >=0) be a Levy process started at 0, with Levy measure nu, and T_x the first hitting time of level x>0: T_x := inf{t>=0; X_t>x}. Let F(theta,mu,rho,.) be the joint Lapl…