1,761 research outputs found
On the finiteness and stability of certain sets of associated primes ideals of local cohomology modules
Let be a Noetherian local ring, an ideal of and a
finitely generated -module. Let be an integer and
r=\depth_k(I,N) the length of a maximal -sequence in dimension in
defined by M. Brodmann and L. T. Nhan ({Comm. Algebra, 36 (2008), 1527-1536).
For a subset S\subseteq \Spec R we set S_{{\ge}k}={\p\in
S\mid\dim(R/\p){\ge}k}. We first prove in this paper that
\Ass_R(H^j_I(N))_{\ge k} is a finite set for all }. Let
\fN=\oplus_{n\ge 0}N_n be a finitely generated graded \fR-module, where
\fR is a finitely generated standard graded algebra over . Let be
the eventual value of \depth_k(I,N_n). Then our second result says that for
all the sets \bigcup_{j{\le}l}\Ass_R(H^j_I(N_n))_{{\ge}k} are
stable for large .Comment: To appear in Communication in Algebr
Generalized Differentiation and Characterizations for Differentiability of Infimal Convolutions
This paper is devoted to the study of generalized differentiation properties
of the infimal convolution. This class of functions covers a large spectrum of
nonsmooth functions well known in the literature. The subdifferential formulas
obtained unify several known results and allow us to characterize the
differentiability of the infimal convolution which plays an important role in
variational analysis and optimization
Parametric Continuity of Stationary Distributions
The paper gives conditions under which stationary distributions of Markov models depend continuously on the parameters. It extends a well-known parametric continuity theorem for compact state space to the unbounded setting of standard econometrics and time series analysis. Applications to several theoretical and estimation problems are outlined.Parametric, Continuity, Stationary Distributions
Walras and Dividends Equilibrium with Possibly Satiated Consumers
The main contribution of the paper is to provide a weaker non-satiation assumption than the one commonly used in the literature to ensure the existence of competitive equilibrium. Our assumption allows for satiation points inside the set of individually feasible consumptions, provided that the consumer has satiation points available to him outside this set. As a result, we show the concept of equilibrium with dividends (See Aumann and Dreze (1986), Mas-Collel (1992)) is pertinent only when the set of satiation points is included in the set of individually feasible consumptions. Our economic motivation stems from the fact that in decentralized markets, increasing the incomes of consumers through dividends, if it is possible, is costly since it involves the intervention of a social planner. Then, we show, in particular, how in securities markets our weak nonsatiation assumption is satisfied by Werner's (1987) assumption.Satiation, Dividends, Equilibrium, Exchange Economy, Short-selling
Equivalent Conditions for Irreducibility of Discrete Time Markov Chains
We consider discrete time Markov chains on general state space. It is shown that a certain property referred to here as nondecomposability is equivalent to irreducibility, and that a Markov chain with invariant distribution is irreducible if and only if the invariant distribution is unique and assigns positive probability to all absorbing sets.
Parametric continuity of stationary distributions
For Markovian economic models, long-run equilibria are typically identified with the stationary (invariant) distributions generated by the model. In this paper weprovide new sufficient conditions for continuity in the map from parameters to these equilibria. Several existing results are shown to be special cases of our theorem.Markov processes, stochastic dynamics, parametric continuity
On the existence of a Ramsey equilibrium with endogenous labor supply and borrowing constraints
In this paper, we study the existence of an intertemporal equilibrium in a Ramsey model with heterogenous discounting, elastic labor supply and borrowing constraints. Applying a fixed-point argument by Gale and Mas-Colell (1975), we prove the existence of an equilibrium in a truncated bounded economy. This equilibrium is also an equilibrium of any unbounded economy with the same fundamentals. Finally, we prove the existence of an equilibrium in an infinite-horizon economy as a limit of a sequence of truncated economies. On the one hand, our paper generalizes Becker et al. (1991) because of the elastic labor supply and, on the other hand, Bosi and Seegmuller (2010) because of a proof of global existence. Our methodology can be also applied to other Ramsey models with different market imperfections.Existence of equilibrium, Ramsey model, heterogeneous agents, endogenous labor supply, borrowing constraint.
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