Results 1  10
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106
Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry
, 2004
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Cooling process for inelastic Boltzmann equations for hard spheres, Part I: The Cauchy Problem
"... We develop the Cauchy theory of the spatially homogeneous inelastic Boltzmann equation for hard spheres, for a general form of collision rate which includes in particular variable restitution coefficients depending on the kinetic energy and the relative velocity. It covers physically realistic mode ..."
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Cited by 25 (8 self)
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We develop the Cauchy theory of the spatially homogeneous inelastic Boltzmann equation for hard spheres, for a general form of collision rate which includes in particular variable restitution coefficients depending on the kinetic energy and the relative velocity. It covers physically realistic models for granular materials. We prove (local in time) nonconcentration estimates in Orlicz spaces, from which we deduce weak stability and existence theorem. Strong stability together with uniqueness is proved under additional smoothness assumption on the initial datum, for a restricted class of collision rates. Concerning the longtime behaviour, we give conditions for the cooling process to occur or not in finite time.
The Large Deviation Principle For Stochastic Processes
, 2002
"... this paper either #(x) = p 1 x p , for some p > 0 or #(x) = e x 1. We also see that under certain conditions, the rate function in the LDP for some certain stochastic processes has the form I(z) = # # # # # # # # M #(z # (t)) dt, if z(0) = 0 and z is absolutely continuous ot ..."
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Cited by 14 (10 self)
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this paper either #(x) = p 1 x p , for some p > 0 or #(x) = e x 1. We also see that under certain conditions, the rate function in the LDP for some certain stochastic processes has the form I(z) = # # # # # # # # M #(z # (t)) dt, if z(0) = 0 and z is absolutely continuous otherwise
Soliton Solutions for Quasilinear Schrödinger Equations
, 2002
"... For a class of quasilinear SchrSdinger equations we establish the existence of ground states of soliton type solutions by a minimization argument. ..."
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Cited by 11 (1 self)
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For a class of quasilinear SchrSdinger equations we establish the existence of ground states of soliton type solutions by a minimization argument.
Nefton: Degenerate complex MongeAmpère equations over compact Kähler manifolds. Preprint. ArXiv 0710.5109
"... Kähler manifolds ..."
CalderónZygmund estimates for higher order systems with p(x)growth
 Math. Z
, 2008
"... m u), D m ∫ 〈 ϕ 〉 dx = F  Ω p(x)−2 F, D m 〉 ϕ dx, for allϕ ∈ C ∞ c (Ω; RN), m> 1, with variable growth exponent p: Ω → (1, ∞) we prove that if F  p(·) ∈ L q loc (Ω) with 1 < q < n n−2 + δ, then Dmu  p(·) ∈ L q loc (Ω). We should note that we prove this implication both in the non–degenerate ..."
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Cited by 6 (3 self)
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m u), D m ∫ 〈 ϕ 〉 dx = F  Ω p(x)−2 F, D m 〉 ϕ dx, for allϕ ∈ C ∞ c (Ω; RN), m> 1, with variable growth exponent p: Ω → (1, ∞) we prove that if F  p(·) ∈ L q loc (Ω) with 1 < q < n n−2 + δ, then Dmu  p(·) ∈ L q loc (Ω). We should note that we prove this implication both in the non–degenerate (µ> 0) and in the degenerate case (µ = 0). 1.
A Unified Framework for Utility Maximization Problems: an Orlicz Space Approach. Forthcoming on
"... We consider a stochastic financial incomplete market where the price processes are described by a vectorvalued semimartingale that is possibly nonlocally bounded. We face the classical problem of utility maximization from terminal wealth, with utility functions that are finitevalued over (a, ∞), a ..."
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Cited by 6 (1 self)
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We consider a stochastic financial incomplete market where the price processes are described by a vectorvalued semimartingale that is possibly nonlocally bounded. We face the classical problem of utility maximization from terminal wealth, with utility functions that are finitevalued over (a, ∞), a ∈ [−∞, ∞), and satisfy weak regularity assumptions. We adopt a class of trading strategies that allows for stochastic integrals that are not necessarily bounded from below. The embedding of the utility maximization problem in Orlicz spaces permits us to formulate the problem in a unified way for both the cases a ∈ R and a = −∞. By duality methods, we prove the existence of solutions to the primal and dual problems and show that a singular component in the pricing functionals may also occur with utility functions finite on the entire real line. 1. Introduction. In
Convex Risk Measures Beyond Bounded Risks, or The Canonical Model Space for
 LawInvariant Risk Measures is L 1 , VIF Working Paper
, 2007
"... Average Value at Risk, welche sich breiter Anwendung in der Versicherungswirtschaft erfreuen. Die in den Anwendungen vorherrschende Klasse konvexer Risikomaße hat die ..."
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Cited by 5 (2 self)
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Average Value at Risk, welche sich breiter Anwendung in der Versicherungswirtschaft erfreuen. Die in den Anwendungen vorherrschende Klasse konvexer Risikomaße hat die
Modified logarithmic Sobolev inequalities on R
, 2008
"... We provide a sufficient condition for a measure on the real line to satisfy a modified logarithmic Sobolev inequality, thus extending the criterion of Bobkov and Götze. Under mild assumptions the condition is also necessary. Concentration inequalities are derived. This completes the picture given in ..."
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Cited by 5 (2 self)
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We provide a sufficient condition for a measure on the real line to satisfy a modified logarithmic Sobolev inequality, thus extending the criterion of Bobkov and Götze. Under mild assumptions the condition is also necessary. Concentration inequalities are derived. This completes the picture given in recent contributions by Gentil, Guillin and Miclo. 1
How to Measure Risk?
 Modelling and Decisions in Economics
, 1999
"... In financial optimization, the future distribution of wealth is projected by methods of statistical estimation and simulation. For making decisions, different wealth distributions have to be compared and the optimal has to be chosen. In this paper we discuss methods of assignining measures for risk ..."
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Cited by 5 (0 self)
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In financial optimization, the future distribution of wealth is projected by methods of statistical estimation and simulation. For making decisions, different wealth distributions have to be compared and the optimal has to be chosen. In this paper we discuss methods of assignining measures for risk (which are to be minimized) and measures for safety (which are to be maximized) to wealth distributions. Some properties of the presented measures are shown. 1 Introduction Decision making in finance is decision making under uncertainity: The outcome of today's decision depends on quantities (like future asset prices, interest rates or exchange rates), which are not known yet. The usual approach to deal with this uncertainity is to represent these quantities by a stochastic model. As a consequence, the outcome of the decision (e.g. the future wealth) is a random variable. Stochasticity of the objective adds a new dimension to the decision making process: Whereas deterministic problems are c...