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6,385
A Variational Representation for Positive Functionals of Infinite Dimensional Brownian Motion
"... A variational representation for positive functionals of a Hilbert space valued Wiener process (W ()) is proved. This representation is then used to prove a large deviations principle for the family {G # (W ())}#>0 where G # is an appropriate family of measurable maps from the Wiener space ..."
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Cited by 43 (7 self)
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to some Polish space. Key Words: Large deviations, Laplace principle, stochastic control, cylindrical Brownian motion, stochastic evolution equations, infinite dimensional stochastic calculus. # This research supported in part by the National Science Foundation (NSFDMI9812857) and the University
Intrinsic volumes of the Brownian motion body, Discrete Comput
 Geom
, 2001
"... Motivated from Gaussian processes, we derive the intrinsic volumes of the infinite–dimensional Brownian motion body. The method is by discretization to a class of orthoschemes. Numerical support is offered for a conjecture of SangwineYager, and another conjecture is offered on the rate of decay of ..."
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Cited by 4 (1 self)
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Motivated from Gaussian processes, we derive the intrinsic volumes of the infinite–dimensional Brownian motion body. The method is by discretization to a class of orthoschemes. Numerical support is offered for a conjecture of SangwineYager, and another conjecture is offered on the rate of decay
Gaussian Measure of a Small Ball and Capacity in Wiener Space
"... Summary. We give asymptotic bounds for the Gaussian measure of a small ball in terms of the hitting probabilities of a suitably chosen infinite dimensional Brownian motion. Our estimates refine earlier works of Erickson [6]. ..."
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Summary. We give asymptotic bounds for the Gaussian measure of a small ball in terms of the hitting probabilities of a suitably chosen infinite dimensional Brownian motion. Our estimates refine earlier works of Erickson [6].
Large deviations for the Boussinesq equations under random influences
 STOCHASTIC PROCESSES APPL
, 2008
"... A Boussinesq model for the Bénard convection under random influences is considered as a system of stochastic partial differential equations. This is a coupled system of stochastic NavierStokes equations and the transport equation for temperature. Large deviations are proved, using a weak converge ..."
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Cited by 17 (6 self)
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convergence approach based on a variational representation of functionals of infinitedimensional Brownian motion.
Abstracts of the talks
, 2007
"... Lower bounds for the density of locally elliptic Itô processes We consider a multidimensional Itô process dirven by an infinite dimensional Brownian motion. We assume regularity in Malliavin sense and we also make a local ellipticity assumption. Under these hypothesis the law of the process is absol ..."
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Lower bounds for the density of locally elliptic Itô processes We consider a multidimensional Itô process dirven by an infinite dimensional Brownian motion. We assume regularity in Malliavin sense and we also make a local ellipticity assumption. Under these hypothesis the law of the process
Entropy Minimization and Schrödinger Processes in Infinite Dimensions
, 1997
"... Schrödinger processes are defined as mixtures of Brownian bridges which preserve the Markov property. In finite dimensions, they can be characterized as htransforms in the sense of Doob for some spacetime harmonic function h of Brownian motion, and also as solutions to a large deviation problem in ..."
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Cited by 5 (0 self)
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introduced by Schrödinger which involves minimization of relative entropy with given marginals. As a basic case study in infinite dimensions, we investigate these different aspects for Schrödinger processes of infinite dimensional Brownian motion. The results and examples concerning entropy minimization
Note on the Schrödinger Equation and IProjections
"... We determine sufficient conditions for the closedness of sum spaces of L¹functions. As a consequence of Csiszar's projection theorem this implies generalizations of results of Fortet, Beurling and Hobby and Pyke on the existence and uniqueness of solutions of some nonlinear integral equations ..."
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equations, which were introduced by Schrödinger, to describe the most probable behaviour of Brownian motions conditional on the observed initial and final state in a finite interval (0; t1). The result is also of interest for a large deviation formula for infinite dimensional Brownian motions related
DIFFEOMORPHISMS OF THE CIRCLE AND BROWNIAN MOTIONS ON AN INFINITEDIMENSIONAL SYMPLECTIC GROUP
, 802
"... Abstract. An embedding of the group Diff(S 1) of orientation preserving diffeomorphims of the unit circle S 1 into an infinitedimensional symplectic group, Sp(∞), is studied. The authors prove that this embedding is not surjective. A Brownian motion is constructed on Sp(∞). This study is motivated ..."
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Cited by 5 (2 self)
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Abstract. An embedding of the group Diff(S 1) of orientation preserving diffeomorphims of the unit circle S 1 into an infinitedimensional symplectic group, Sp(∞), is studied. The authors prove that this embedding is not surjective. A Brownian motion is constructed on Sp(∞). This study is motivated
Ito ̂ formula for the infinitedimensional fractional Brownian motion
, 2005
"... We introduce the stochastic integration with respect to the infinitedimensional fractional Brownian motion. Using the techniques of the anticipating stochastic calculus, we derive an Ito ̂ formula for Hurst parameter bigger than 12. 1 ..."
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Cited by 1 (0 self)
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We introduce the stochastic integration with respect to the infinitedimensional fractional Brownian motion. Using the techniques of the anticipating stochastic calculus, we derive an Ito ̂ formula for Hurst parameter bigger than 12. 1
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
Results 1  10
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6,385