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183,202
A RiskFactor Model Foundation for RatingsBased Bank Capital Rules
 Journal of Financial Intermediation
, 2003
"... When economic capital is calculated using a portfolio model of credit valueatrisk, the marginal capital requirement for an instrument depends, in general, on the properties of the portfolio in which it is held. By contrast, ratingsbased capital rules, including both the current Basel Accord and i ..."
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Cited by 283 (1 self)
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When economic capital is calculated using a portfolio model of credit valueatrisk, the marginal capital requirement for an instrument depends, in general, on the properties of the portfolio in which it is held. By contrast, ratingsbased capital rules, including both the current Basel Accord
Variance Reduction in Stochastic Homogenization Using Antithetic Variables
, 2011
"... Abstract. Some theoretical issues related to the problem of variance reduction in numerical approaches for stochastic homogenization are examined. On some simple, yet representative cases, it is demonstrated theoretically that a technique based on antithetic variables can indeed reduce the variance ..."
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Cited by 8 (4 self)
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Abstract. Some theoretical issues related to the problem of variance reduction in numerical approaches for stochastic homogenization are examined. On some simple, yet representative cases, it is demonstrated theoretically that a technique based on antithetic variables can indeed reduce the variance
Multi Level Monte Carlo methods with Control Variate for elliptic Stochastic Partial Differential Equations
"... We consider the numerical approximation of a partial differential equation (PDE) with random coefficients. These type of problems can be found in many applications in which the lack of available measurements makes an accurate reconstruction of the coefficients appearing in the mathematical model un ..."
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unfeasible. In particular we focus on the model problem of an elliptic partial differential equation with random diffusion coefficient, modeled as a random field with limited spatial regularity. This approach is inspired by the groundwater flow problem which has a great importance in hydrology
ROBUST VARIANCE REDUCTION FOR RANDOM WALK METHODS ∗
"... Abstract. Random walk methods are effective for solving linear partial differential equations in many dimensions, especially those involving complex geometries. They are based on an equivalence given by a Feynman–Kac formula between an expectation of a functional of a stochastic process and the solu ..."
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Cited by 2 (0 self)
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and the solution at a point of a partial differential equation. The drawback is that the error is proportional only to the square root of the reciprocal of the number of trials. Efficiency depends critically on variance reduction. A general strategy for doing this in the case of stochastic differential equations
Building blocks for computer vision with stochastic partial differential equations
 Int J. Comput. Vis
, 2008
"... Abstract We discuss the basic concepts of computer vision with stochastic partial differential equations (SPDEs). In typical approaches based on partial differential equations (PDEs), the end result in the best case is usually one value per pixel, the “expected ” value. Error estimates or even full ..."
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Cited by 1 (0 self)
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Abstract We discuss the basic concepts of computer vision with stochastic partial differential equations (SPDEs). In typical approaches based on partial differential equations (PDEs), the end result in the best case is usually one value per pixel, the “expected ” value. Error estimates or even full
AN OPTIMAL VARIANCE ESTIMATE IN STOCHASTIC HOMOGENIZATION OF DISCRETE ELLIPTIC EQUATIONS
, 2012
"... An optimal variance estimate in stochastic ..."
Systems of Stochastic Partial Differential Equations
, 2013
"... This work is motivated by constructing a weather simulator for precipitation. Temperature and humidity are two of the most important driving forces of precipitation, and the strategy is to have a stochastic model for temperature and humidity, and use a deterministic model to go from these variables ..."
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This work is motivated by constructing a weather simulator for precipitation. Temperature and humidity are two of the most important driving forces of precipitation, and the strategy is to have a stochastic model for temperature and humidity, and use a deterministic model to go from these variables
Combined Physical/Stochastic Space for Stochastic Differential Equations
, 2012
"... Abstract: In the present work, an innovative method for solving stochastic partial differential equations is presented. A multiresolution method permitting to compute statistics of the quantity of interest for a whatever form of the probability density function is extended to permit an adaptation in ..."
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Abstract: In the present work, an innovative method for solving stochastic partial differential equations is presented. A multiresolution method permitting to compute statistics of the quantity of interest for a whatever form of the probability density function is extended to permit an adaptation
Results 1  10
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183,202