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MARTINGALE PROPERTY OF GENERALIZED STOCHASTIC EXPONENTIALS
"... Abstract. For a real Borel measurable function b, which satisfies certain integrability conditions, it is possible to define a stochastic integral of the process b(Y) with respect to a Brownian motion W, where Y is a diffusion driven by W. It is well know that the stochastic exponential of this stoc ..."
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Abstract. For a real Borel measurable function b, which satisfies certain integrability conditions, it is possible to define a stochastic integral of the process b(Y) with respect to a Brownian motion W, where Y is a diffusion driven by W. It is well know that the stochastic exponential
Stochastic exponential integrators for the finite element discretization of SPDEs
, 2010
"... We consider the numerical approximation of general semilinear parabolic stochastic partial differential equations (SPDEs) driven by additive spacetime noise. In contrast to the standard time stepping methods which uses basic increments of the noise and the approximation of the exponential functio ..."
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Cited by 8 (2 self)
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We consider the numerical approximation of general semilinear parabolic stochastic partial differential equations (SPDEs) driven by additive spacetime noise. In contrast to the standard time stepping methods which uses basic increments of the noise and the approximation of the exponential
ON CRITERIA FOR THE UNIFORM INTEGRABILITY OF BROWNIAN STOCHASTIC EXPONENTIALS
"... Abstract. This paper deals with various sufficient (as well as necessary and sufficient) conditions for the uniform integrability of the exponential martingales of the form Zt = exp Bt∧τ − 1 ..."
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Cited by 4 (0 self)
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Abstract. This paper deals with various sufficient (as well as necessary and sufficient) conditions for the uniform integrability of the exponential martingales of the form Zt = exp Bt∧τ − 1
Tail behavior or random products and stochastic exponentials
, 2007
"... In this paper we study the distributional tail behavior of the solution to a linear stochastic differential equation driven by infinite variance αstable Lévy motion. We show that the solution is regularly varying with index α. An important step in the proof is the study of a Poisson number of prod ..."
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Cited by 3 (2 self)
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In this paper we study the distributional tail behavior of the solution to a linear stochastic differential equation driven by infinite variance αstable Lévy motion. We show that the solution is regularly varying with index α. An important step in the proof is the study of a Poisson number
Articulated body motion capture by annealed particle filtering
 In IEEE Conf. on Computer Vision and Pattern Recognition
, 2000
"... The main challenge in articulated body motion tracking is the large number of degrees of freedom (around 30) to be recovered. Search algorithms, either deterministic or stochastic, that search such a space without constraint, fall foul of exponential computational complexity. One approach is to intr ..."
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Cited by 494 (4 self)
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The main challenge in articulated body motion tracking is the large number of degrees of freedom (around 30) to be recovered. Search algorithms, either deterministic or stochastic, that search such a space without constraint, fall foul of exponential computational complexity. One approach
Lower and Upper Bounds on the Generalization of Stochastic Exponentially Concave Optimization
"... In this paper we derive high probability lower and upper bounds on the excess risk of stochastic optimization of exponentially concave loss functions. Exponentially concave loss functions encompass several fundamental problems in machine learning such as squared loss in linear regression, logistic ..."
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In this paper we derive high probability lower and upper bounds on the excess risk of stochastic optimization of exponentially concave loss functions. Exponentially concave loss functions encompass several fundamental problems in machine learning such as squared loss in linear regression, logistic
Errata of “Lower and Upper Bounds on the Generalization of Stochastic Exponentially Concave Optimization”
, 2015
"... We fix two typos in the statement of Theorem 4, and an error in Theorem 8. To be more clear, we rewrite the proof of the lower bound. ..."
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We fix two typos in the statement of Theorem 4, and an error in Theorem 8. To be more clear, we rewrite the proof of the lower bound.
The WienerAskey Polynomial Chaos for Stochastic Differential Equations
 SIAM J. SCI. COMPUT
, 2002
"... We present a new method for solving stochastic differential equations based on Galerkin projections and extensions of Wiener's polynomial chaos. Specifically, we represent the stochastic processes with an optimum trial basis from the Askey family of orthogonal polynomials that reduces the dime ..."
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Cited by 398 (42 self)
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the dimensionality of the system and leads to exponential convergence of the error. Several continuous and discrete processes are treated, and numerical examples show substantial speedup compared to MonteCarlo simulations for low dimensional stochastic inputs.
Rapid solution of problems by quantum computation
 IN PROC
, 1992
"... A class of problems is described which can be solved more efficiently by quantum computation than by any classical or stochastic method. The quantum computation solves the problem with certainty in exponentially less time than any classical deterministic computation. ..."
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Cited by 441 (4 self)
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A class of problems is described which can be solved more efficiently by quantum computation than by any classical or stochastic method. The quantum computation solves the problem with certainty in exponentially less time than any classical deterministic computation.
Results 1  10
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2,451