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Intensity process and compensator: A new filtration expansion approach and the Jeulin–Yor theorem. The Annals of Applied Probability
, 2007
"... Let (Xt)t≥0 be a continuoustime, timehomogeneous strong Markov process with possible jumps and let τ be its first hitting time of a Borel subset of the state space. Suppose X is sampled at random times and suppose also that X has not hit the Borel set by time t. What is the intensity process of τ ..."
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Cited by 16 (2 self)
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based on this information? This question from credit risk encompasses basic mathematical problems concerning the existence of an intensity process and filtration expansions, as well as some conceptual issues for credit risk. By revisiting and extending the famous Jeulin–Yor [Lecture Notes in Math. 649
due to Saisho, Tanemura and Yor of Pitman’s theorem
"... On the martingales obtained by an extension ..."
ON BALAZARD, SAIAS, AND YOR’S EQUIVALENCE TO THE RIEMANN HYPOTHESIS
"... Abstract. Balazard, Saias, and Yor proved that the Riemann Hypothesis is equivalent to a certain weighted integral of the logarithm of the Riemann zetafunction along the critical line equaling zero. Assuming the Riemann Hypothesis, we investigate the rate at which a truncated version of this integr ..."
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Abstract. Balazard, Saias, and Yor proved that the Riemann Hypothesis is equivalent to a certain weighted integral of the logarithm of the Riemann zetafunction along the critical line equaling zero. Assuming the Riemann Hypothesis, we investigate the rate at which a truncated version
ELECTRONIC COMMUNICATIONS in PROBABILITY Limits of renewal processes and PitmanYor distribution
"... We consider a renewal process with regularly varying stationary and weakly dependent steps, and prove that the steps made before a given time t, satisfy an interesting invariance principle. Namely, together with the age of the renewal process at time t, they converge after scaling to the Pitman–Yor ..."
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We consider a renewal process with regularly varying stationary and weakly dependent steps, and prove that the steps made before a given time t, satisfy an interesting invariance principle. Namely, together with the age of the renewal process at time t, they converge after scaling to the Pitman–Yor
An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions
, 1996
"... this paper, we denote by #Z t # t#0 a normalized fractional Brownian motion #FBM# with selfsimilarity parameter H #0; 1#, characterized by the following properties: #i# Z t has stationary increments; #ii# Z 0 =0, and EZ t =0for all t; #iii# EZ jtj for all t; #iv# Z t is Gaussian; #v# Z t h ..."
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Cited by 81 (12 self)
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follows from Kolmogorov's criterion for the continuity of sample paths, see Revuz and Yor 1991#: Theorem 1.1 The sample paths of a continuous fractional Brownian motion with parameter H are, outside a negligible event, H#lder continuous with every exponent # #H. When H = 2f1=2; 1g, the FBM
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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Cited by 45 (2 self)
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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
RayKnight theorems via continuous trees
"... this paper, we are interested in obtaining the generalized RayKnight theorems (previously proved by Yor [10]) using branching processes. It was already observed in O'Connell's thesis [6] that the construction of the natural tree associated to Brownian excursion (Le Gall [4], NeveuPitman ..."
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Cited by 1 (0 self)
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this paper, we are interested in obtaining the generalized RayKnight theorems (previously proved by Yor [10]) using branching processes. It was already observed in O'Connell's thesis [6] that the construction of the natural tree associated to Brownian excursion (Le Gall [4], Neveu
On the stochastic behaviour of optional processes up to random times
 Forthcoming in the Annals of Applied Probability
, 2014
"... In this paper, a study of random times on filtered probability spaces is undertaken. The main message is that, as long as distributional properties of optional processes up to the random time are involved, there is no loss of generality in assuming that the random time is actually a randomised stopp ..."
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Cited by 2 (1 self)
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as up to lastpassage times over finite intervals. Furthermore, a novel proof of the Jeulin–Yor decomposition formula via Girsanov’s theorem is provided. Introduction. Consider a filtered measurable space (,F), where F = (Ft)t∈R+ is a rightcontinuous filtration, as well as an underlying sigmaalgebra F
SOME RANDOM TIMES AND MARTINGALES ASSOCIATED WITH BES0(δ) PROCESSES (0 < δ < 2)
, 2007
"... Abstract. In this paper, we study Bessel processes of dimension δ ≡ 2(1 − µ), with 0 < δ < 2, and some related martingales and random times. Our approach is based on martingale techniques and the general theory of stochastic processes (unlike the usual approach based on excursion theory), alth ..."
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Cited by 1 (1 self)
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), although for 0 < δ < 1, these processes are even not semimartingales. The last time before 1 when a Bessel process hits 0, called gµ, plays a key role in our study: we characterize its conditional distribution and extend Paul Lévy’s arc sine law and a related result of Jeulin about the standard
Lamperti’s representation theorem [5] applied to E (−ν)
, 806
"... Abstract. We show how a description of Brownian exponential functionals as a renewal series gives access to the law of the hitting time of a squareroot boundary by a Bessel process. This extends classical results by Breiman and Shepp, concerning Brownian motion, and recovers by different means, ext ..."
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, extensions for Bessel processes, obtained independently by Delong and Yor. Let Bt be the standard real valued Brownian motion and for ν> 0, introduce the geometric Brownian motion E (−ν) t and its exponential functional A (−ν) t
Results 1  10
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25