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5,998
Robot Motion Planning: A Distributed Representation Approach
, 1991
"... We propose a new approach to robot path planning that consists of building and searching a graph connecting the local minima of a potential function defined over the robot’s configuration space. A planner based on this approach has been implemented. This planner is considerably faster than previous ..."
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Cited by 402 (26 self)
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of these techniques is a Monte Carlo technique that escapes local minima by executing Brownian motions. The overall approach is made possible by the systematic use of distributed representations (bitmaps) for the robot’s work space and configuration space. We have experimented with the planner using several computer
The Variance Gamma Process and Option Pricing.
 European Finance Review
, 1998
"... : A three parameter stochastic process, termed the variance gamma process, that generalizes Brownian motion is developed as a model for the dynamics of log stock prices. The process is obtained by evaluating Brownian motion with drift at a random time given by a gamma process. The two additional par ..."
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Cited by 365 (34 self)
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: A three parameter stochastic process, termed the variance gamma process, that generalizes Brownian motion is developed as a model for the dynamics of log stock prices. The process is obtained by evaluating Brownian motion with drift at a random time given by a gamma process. The two additional
Stochastic Analysis of the Fractional Brownian Motion
 POTENTIAL ANALYSIS
, 1996
"... Since the fractional Brownian motion is not a semimartingale, the usual Itô calculus cannot be used to define a full stochastic calculus. However, in this work, we obtain the Itô formula, the ItôClark representation formula and the Girsanov theorem for the functionals of a fractional Brownian motio ..."
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Cited by 199 (11 self)
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Since the fractional Brownian motion is not a semimartingale, the usual Itô calculus cannot be used to define a full stochastic calculus. However, in this work, we obtain the Itô formula, the ItôClark representation formula and the Girsanov theorem for the functionals of a fractional Brownian
The twoparameter PoissonDirichlet distribution derived from a stable subordinator.
, 1995
"... The twoparameter PoissonDirichlet distribution, denoted pd(ff; `), is a distribution on the set of decreasing positive sequences with sum 1. The usual PoissonDirichlet distribution with a single parameter `, introduced by Kingman, is pd(0; `). Known properties of pd(0; `), including the Markov ..."
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Cited by 356 (33 self)
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of Brownian motion and Bessel processes. For 0 ! ff ! 1, pd(ff; 0) is the asymptotic distribution of ranked lengths of excursions of a Markov chain away from a state whose recurrence time distribution is in the domain of attraction of a stable law of index ff. Formulae in this case trace back to work
Experimental Queueing Analysis with LongRange Dependent Packet Traffic
 IEEE/ACM Transactions on Networking
, 1996
"... Recent traffic measurement studies from a wide range of working packet networks have convincingly established the presence of significant statistical features that are characteristic of fractal traffic processes, in the sense that these features span many time scales. Of particular interest in packe ..."
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Cited by 346 (14 self)
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impact on queueing performance, and is a dominant characteristic for a number of packet traffic engineering problems. In addition, we give conditions under which the use of compact and simple traffic models that incorporate longrange dependence in a parsimonious manner (e.g., fractional Brownian motion
Term structures of credit spreads with incomplete accounting information
 ECONOMETRICA
, 2001
"... We study the implications of imperfect information for term structures of credit spreads on corporate bonds. We suppose that bond investors cannot observe the issuer’s assets directly, and receive instead only periodic and imperfect accounting reports. For a setting in which the assets of the firm ..."
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Cited by 317 (19 self)
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of the firm are a geometric Brownian motion until informed equityholders optimally liquidate, we derive the conditional distribution of the assets, given accounting data and survivorship. Contrary to the perfectinformation case, there exists a defaultarrival intensity process. That intensity is calculated
Nonintersecting Planar Brownian Motions
, 1995
"... In this paper we construct a measure on pairs of Brownian motions starting at the same point conditioned so their paths do not intersect. The construction of this measure is a start towards the rigorous understanding of nonintersecting Brownian motions as a conformal field. Let B 1 ; B 2 be inde ..."
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Cited by 16 (7 self)
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be independent Brownian motions in R 2 starting at distinct points on the unit circle. Let T j r be the first time that the jth Brownian motion reaches distance r and let D r be the event D r = fB 1 [0; T 1 e r ] " B 2 [0; T 2 e r ] = ;g: We construct the measure by considering the limit
Stochastic Calculus for Fractional Brownian Motion. I: Theory
 SIAM J. Control optim
, 1999
"... This paperd=R+3# es some of the results in [5] for a stochastic calculus for a fractional Brownian motion with the Hurst parameter in the interval (1/2, 1). Two stochastic integrals aredeg=z with explicit expressions for their first two moments. Multipleand iterated integrals of a fractional Browini ..."
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Cited by 188 (16 self)
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This paperd=R+3# es some of the results in [5] for a stochastic calculus for a fractional Brownian motion with the Hurst parameter in the interval (1/2, 1). Two stochastic integrals aredeg=z with explicit expressions for their first two moments. Multipleand iterated integrals of a fractional
Exponential functionals of Brownian motion. II. Some related diffusion processes,
 Probab. Surv.
, 2005
"... Abstract: 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 ..."
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Cited by 199 (16 self)
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Abstract: 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
Results 1  10
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5,998