2,285 research outputs found
Large Deviations for Stochastic Generalized Porous Media Equations
The large deviation principle is established for the distributions of a class
of generalized stochastic porous media equations for both small noise and short
time.Comment: 15 pages; BiBoS-Preprint No. 05-11-196; publication in preparatio
Transportation-information inequalities for Markov processes (II) : relations with other functional inequalities
We continue our investigation on the transportation-information inequalities
for a symmetric markov process, introduced and studied in \cite{GLWY}.
We prove that implies the usual transportation inequalities , then
the corresponding concentration inequalities for the invariant measure .
We give also a direct proof that the spectral gap in the space of Lipschitz
functions for a diffusion process implies (a result due to \cite{GLWY})
and a Cheeger type's isoperimetric inequality. Finally we exhibit relations
between transportation-information inequalities and a family of functional
inequalities (such as -log Sobolev or -Sobolev)
CMNet: a novel model and design rationale based on comparison studies and synergy of CNN and MetaFormer
Permanence and Stability of an Age-Structured Prey-Predator System with Delays
An age-structured prey-predator model with delays is proposed and analyzed. Mathematical analyses of the model equations with regard to boundedness of solutions, permanence, and stability are analyzed. By using the persistence theory for infinite-dimensional systems, the sufficient conditions for the permanence of the system are obtained. By constructing suitable Lyapunov functions and using an iterative technique, sufficient conditions are also obtained for the global asymptotic stability of the positive equilibrium of the model
Lyapunov conditions for logarithmic Sobolev and Super Poincaré inequality
International audienceWe show how to use Lyapunov functions to obtain functional inequalities which are stronger than Poincaré inequality (for instance logarithmic Sobolev or -Sobolev). The case of Poincaré and weak Poincaré inequalities was studied in Bakry and al. This approach allows us to recover and extend in an unified way some known criteria in the euclidean case (Bakry-Emery, Wang, Kusuoka-Stroock ...)
Leader-follower Game in VMI System with Limited Production Capacity Considering Wholesale and Retail Prices
VMI (Vendor Managed Inventory) is a widely used cooperative inventory policy in supply chains in which each enterprise has its autonomy in pricing. This paper discusses a leader-follower Stackelberg game in a VMI supply chain where the manufacturer, as a leader, produces a single product with a limited production capacity and delivers it at a wholesale price to multiple different retailers, as the followers, who then sell the product in dispersed and independent markets at retail prices. An algorithm is then developed to determine the equilibrium of the Stackelberg game. Finally, a numerical study is conducted to understand the influence of the Stackelberg equilibrium and market related parameters on the profits of the manufacturer and its retailers. Through the numerical example, our research demonstrates that: (a) the market related parameters have significant influence on the manufacturer’ and its retailers’ profits; (b) a retailer’s profit ma
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