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On some exponential functionals of Brownian motion
 Adv. Appl. Prob
, 1992
"... Abstract: This is the second part of our survey on exponential functionals of Brownian motion. We focus on the applications of the results about the distributions of the exponential functionals, which have been discussed in the first part. Pricing formula for call options for the Asian options, expl ..."
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Cited by 98 (9 self)
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Abstract: This is the second part of our survey on exponential functionals of Brownian motion. We focus on the applications of the results about the distributions of the exponential functionals, which have been discussed in the first part. Pricing formula for call options for the Asian options, explicit expressions for the heat kernels on hyperbolic spaces, diffusion processes in random environments and extensions of Lévy’s and Pitman’s theorems are discussed.
Exponential functionals of Lévy processes
 Probabilty Surveys
, 2005
"... Abstract: This text surveys properties and applications of the exponential functional ∫ t exp(−ξs)ds of realvalued Lévy processes ξ = (ξt, t ≥ 0). 0 ..."
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Cited by 34 (4 self)
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Abstract: This text surveys properties and applications of the exponential functional ∫ t exp(−ξs)ds of realvalued Lévy processes ξ = (ξt, t ≥ 0). 0
Limiting laws for long Brownian bridges perturbed by their onesided maximum
 III, in "Period. Math. Hungar
"... In homage to Professors E. Csaki and P. Revesz. Abstract. Results of penalization of a onedimensional Brownian motion (Xt), by its onesided maximum (St = Xu), which were recently obtained by the authors are improved with the sup 0≤u≤t considerationin the present paper of the asymptotic behaviour ..."
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Cited by 3 (2 self)
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In homage to Professors E. Csaki and P. Revesz. Abstract. Results of penalization of a onedimensional Brownian motion (Xt), by its onesided maximum (St = Xu), which were recently obtained by the authors are improved with the sup 0≤u≤t considerationin the present paper of the asymptotic behaviour of the likewise penalized Brownian bridges of length t, as t → ∞, or penalizations by functions of (St, Xt), and also the study of the speed of convergence, as t → ∞, of the penalized distributions at time t.
EXPONENTIAL MARTINGALES AND TIME INTEGRALS OF BROWNIAN MOTION
, 2007
"... Abstract. We find a simple expression for the probability density of R exp(Bs − s/2)ds in terms of its distribution function and the distribution function for the time integral of exp(Bs + s/2). The relation is obtained with a change of measure argument where expectations over events determined by t ..."
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Cited by 1 (1 self)
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Abstract. We find a simple expression for the probability density of R exp(Bs − s/2)ds in terms of its distribution function and the distribution function for the time integral of exp(Bs + s/2). The relation is obtained with a change of measure argument where expectations over events determined by the time integral are replaced by expectations over the entire probability space. We develop precise information concerning the lower tail probabilities for these random variables as well as for time integrals of geometric Brownian motion with arbitrary constant drift. In particular, E [ exp ` θ / R exp(Bs)ds ´ ] is finite iff θ < 2. We present a new formula for the price of an Asian call option.
ELECTRONIC COMMUNICATIONS in PROBABILITY FURTHER EXPONENTIAL GENERALIZATION OF PITMAN’S 2MX THEOREM
, 2001
"... Diffusion processes, Exponential analogue of the 2M − X Pitman’s theorem We present a class of processes which enjoy an exponential analogue of Pitman’s 2MX theorem, improving hence some works of H. Matsumoto and M. Yor. 1 ..."
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Diffusion processes, Exponential analogue of the 2M − X Pitman’s theorem We present a class of processes which enjoy an exponential analogue of Pitman’s 2MX theorem, improving hence some works of H. Matsumoto and M. Yor. 1
Littelmann paths and Brownian paths
, 2004
"... Abstract. We study some path transformations related to Littelmann path model and their applications to representation theory and Brownian motion in a Weyl chamber. 1. ..."
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Abstract. We study some path transformations related to Littelmann path model and their applications to representation theory and Brownian motion in a Weyl chamber. 1.
Some explicit Krein
, 2005
"... representations of certain subordinators, including the Gamma process ..."
Directed polymers and the quantum Toda lattice
, 2009
"... We give a characterization of the law of the partition function of a Brownian directed polymer model in terms of the eigenfunctions of the quantum Toda lattice. This is obtained via a multidimensional generalization of theorem of Matsumoto and Yor concerning exponential functionals of Brownian motio ..."
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We give a characterization of the law of the partition function of a Brownian directed polymer model in terms of the eigenfunctions of the quantum Toda lattice. This is obtained via a multidimensional generalization of theorem of Matsumoto and Yor concerning exponential functionals of Brownian motion.