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23
New results in linear filtering and prediction theory
 TRANS. ASME, SER. D, J. BASIC ENG
, 1961
"... A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary sta ..."
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A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary statistics. The variance equation is closely related to the Hamiltonian (canonical) differential equations of the calculus of variations. Analytic solutions are available in some cases. The significance of the variance equation is illustrated by examples which duplicate, simplify, or extend earlier results in this field. The Duality Principle relating stochastic estimation and deterministic control problems plays an important role in the proof of theoretical results. In several examples, the estimation problem and its dual are discussed sidebyside. Properties of the variance equation are of great interest in the theory of adaptive systems. Some aspects of this are considered briefly.
Rational Inattention and Portfolio Selection
 Journal of Finance
, 2007
"... †Corresponding author. ..."
GENERALIZED RICCI CURVATURE BOUNDS FOR THREE DIMENSIONAL CONTACT SUBRIEMANNIAN MANIFOLDS
, 903
"... Abstract. Measure contraction property is one of the possible generalizations of Ricci curvature bound to more general metric measure spaces. In this paper, we discover sufficient conditions for a three dimensional contact subriemannian manifold to satisfy this property. 1. ..."
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Abstract. Measure contraction property is one of the possible generalizations of Ricci curvature bound to more general metric measure spaces. In this paper, we discover sufficient conditions for a three dimensional contact subriemannian manifold to satisfy this property. 1.
Exact and high order discretization schemes for Wishart processes and their affine extensions, submitted paper. Arxiv Preprint
, 2010
"... This work deals with the simulation of Wishart processes and affine diffusions on positive semidefinite matrices. To do so, we focus on the splitting of the infinitesimal generator, in order to use composition techniques as Ninomiya and Victoir [20] or Alfonsi [1]. Doing so, we have found a remarkab ..."
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Cited by 8 (3 self)
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This work deals with the simulation of Wishart processes and affine diffusions on positive semidefinite matrices. To do so, we focus on the splitting of the infinitesimal generator, in order to use composition techniques as Ninomiya and Victoir [20] or Alfonsi [1]. Doing so, we have found a remarkable splitting for Wishart processes that enables us to sample exactly Wishart distributions, without any restriction on the parameters. It is related but extends existing exact simulation methods based on Bartlett’s decomposition. Moreover, we can construct highorder discretization schemes for Wishart processes and secondorder schemes for general affine diffusions. These schemes are in practice faster than the exact simulation to sample entire paths. Numerical results on their convergence are given.
BISHOP AND LAPLACIAN COMPARISON THEOREMS ON THREE DIMENSIONAL CONTACT SUBRIEMANNIAN MANIFOLDS WITH SYMMETRY
"... Abstract. We prove a Bishop volume comparison theorem and a Laplacian comparison theorem for three dimensional contact subriemannian manifolds with symmetry. 1. ..."
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Abstract. We prove a Bishop volume comparison theorem and a Laplacian comparison theorem for three dimensional contact subriemannian manifolds with symmetry. 1.
The Explicit Laplace Transform for the Wishart Process
 Journal of Applied Probability
, 2014
"... We derive the explicit formula for the joint Laplace transform of the Wishart process and its time integral which extends the original approach of Bru (1991). We compare our methodology with the alternative results given by the variation of constants method, the linearization of the Matrix Riccati O ..."
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Cited by 7 (2 self)
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We derive the explicit formula for the joint Laplace transform of the Wishart process and its time integral which extends the original approach of Bru (1991). We compare our methodology with the alternative results given by the variation of constants method, the linearization of the Matrix Riccati ODE’s and the RungeKutta algorithm. The new formula turns out to be fast and accurate.
A convenient coordinatization of SiegelJacobi domains
 REV. MATH. PHYS
, 2012
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Portfolio Selection with Return Predictability and Periodically Observable Predictive Variables ∗
"... in St. Louis and 2003 MFA Conference for helpful comments. Portfolio Selection with Return Predictability and ..."
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in St. Louis and 2003 MFA Conference for helpful comments. Portfolio Selection with Return Predictability and
SOLUTIONS OF CERTAIN MATRIX EQUATIONS WITH APPLICATIONS TO ENGINEERING SCIENCES
, 1976
"... p) U’ ..."