Abstract
The problem of establishing Hadamard-type inequalities for convex functions on d-dimensional convex bodies (d ≥ 2) translates into the problem of finding appropriate majorants of the involved random vector for the usual convex order. In this work, we use a stochastic approach based on the Brownian motion to establish a multidimensional version of the classical Hadamard inequality. The main result is closely related to the Dirichlet problem and is applied to obtain inequalities for harmonic functions on general convex bodies.
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de la Cal, J., Cárcamo, J., Escauriaza, L. (2010). Hadamard Majorants for the Convex Order and Applications. In: Borgelt, C., et al. Combining Soft Computing and Statistical Methods in Data Analysis. Advances in Intelligent and Soft Computing, vol 77. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14746-3_19
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DOI: https://doi.org/10.1007/978-3-642-14746-3_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14745-6
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