1,761 research outputs found

    On the finiteness and stability of certain sets of associated primes ideals of local cohomology modules

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    Let (R,m)(R,\frak{m}) be a Noetherian local ring, II an ideal of RR and NN a finitely generated RR-module. Let k1k{\ge}-1 be an integer and r=\depth_k(I,N) the length of a maximal NN-sequence in dimension >k>k in II 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 jrj{\le}r}. 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 R0=RR_0=R. Let rr be the eventual value of \depth_k(I,N_n). Then our second result says that for all lrl{\le}r the sets \bigcup_{j{\le}l}\Ass_R(H^j_I(N_n))_{{\ge}k} are stable for large nn.Comment: To appear in Communication in Algebr

    Generalized Differentiation and Characterizations for Differentiability of Infimal Convolutions

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    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

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    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

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    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

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    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

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    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

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    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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