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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.
A REPRESENTATION FOR NONCOLLIDING RANDOM WALKS
 ELECTRONIC COMMUNICATIONS IN PROBABILITY
, 2002
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Random matrices, noncolliding processes and queues
 TO APPEAR IN SÉMINAIRE DE PROBABILITÉS XXXVI
, 2002
"... This is survey of some recent results connecting random matrices, noncolliding processes and queues. ..."
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Cited by 21 (2 self)
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This is survey of some recent results connecting random matrices, noncolliding processes and queues.
On the free energy of a directed polymer in a Brownian environment
, 2006
"... We prove a formula conjectured in [14] for the free energy density of a directed polymer in a Brownian environment in 1 + 1 dimensions. Mathematics Subject Classification (2000): 60K37,82D30,60K25,60J65 1 ..."
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Cited by 6 (0 self)
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We prove a formula conjectured in [14] for the free energy density of a directed polymer in a Brownian environment in 1 + 1 dimensions. Mathematics Subject Classification (2000): 60K37,82D30,60K25,60J65 1
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.
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.