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Seppo Honkapohja  One of the best experts on this subject based on the ideXlab platform.

expectations and the Stability Problem for optimal monetary policies
The Review of Economic Studies, 2003CoAuthors: George W Evans, Seppo HonkapohjaAbstract:Eine auf den Fundamentaldaten beruhende Regelbindung der Geldpolitik ohne Selbstverpflichtung, die bei vollkommen rationalen Erwartungen der privaten Akteure optimal ware, ist instabil, wenn diese Akteure de facto den ublichen Regeln des adaptiven Lernens folgen. Dieses Problem lasst sich dadurch beheben, dass die Erwartungen privater Akteure berucksichtigt und in geeigneter Weise in die optimale Geldpolitik einbezogen werden. Diese eindeutige Schlusfolgerung gilt auch dann, wenn sich der geldpolitische Entscheidungstrager und die privaten Akteure in einem simultanen Lernprozess befinden. Unsere Ergebnisse zeigen, wie wichtig es ist, die Geldpolitik angemessen zu gestalten und dabei nicht nur die Fundamentaldaten, sondern auch direkt die beobachteten Erwartungen privater Haushalte und Unternehmen zu berucksichtigen.

expectations and the Stability Problem for optimal monetary policies
Social Science Research Network, 2001CoAuthors: George W Evans, Seppo HonkapohjaAbstract:A fundamentals based monetary policy rule, which would be the optimal monetary policy without commitment when private agents have perfectly rational expectations, is unstable if in fact these agents follow standard adaptive learning rules. This Problem can be overcome if private expectations are observed and suitable incorporated into the policy maker's optimal rule. These strong results extend to the case in which there is simultaneous learning by the policy maker and the private agents. Our findings show the importance of conditioning policy appropriately, not just on fundamentals, but also directly on observed household and firm expectations.

expectations and the Stability Problem for optimal monetary policies
Research Papers in Economics, 2000CoAuthors: George W Evans, Seppo HonkapohjaAbstract:A fundamentals based monetary policy rule, which would be the optimal monetary policy without commitment when private agents have perfectly rational expectations, is unstable if in fact these agents follow standard adaptive learning rules. This Problem can be overcome if private expectations are observed and suitably incorporated into the policy maker's optimal rule. These strong results extend to the case in which there is simultaneous learning by the policy maker and the private agents. Our findings show the importance of conditioning policy appropriately, not just on fundamentals, but also directly on observed household and firm expectations.
George W Evans  One of the best experts on this subject based on the ideXlab platform.

expectations and the Stability Problem for optimal monetary policies
The Review of Economic Studies, 2003CoAuthors: George W Evans, Seppo HonkapohjaAbstract:Eine auf den Fundamentaldaten beruhende Regelbindung der Geldpolitik ohne Selbstverpflichtung, die bei vollkommen rationalen Erwartungen der privaten Akteure optimal ware, ist instabil, wenn diese Akteure de facto den ublichen Regeln des adaptiven Lernens folgen. Dieses Problem lasst sich dadurch beheben, dass die Erwartungen privater Akteure berucksichtigt und in geeigneter Weise in die optimale Geldpolitik einbezogen werden. Diese eindeutige Schlusfolgerung gilt auch dann, wenn sich der geldpolitische Entscheidungstrager und die privaten Akteure in einem simultanen Lernprozess befinden. Unsere Ergebnisse zeigen, wie wichtig es ist, die Geldpolitik angemessen zu gestalten und dabei nicht nur die Fundamentaldaten, sondern auch direkt die beobachteten Erwartungen privater Haushalte und Unternehmen zu berucksichtigen.

expectations and the Stability Problem for optimal monetary policies
Social Science Research Network, 2001CoAuthors: George W Evans, Seppo HonkapohjaAbstract:A fundamentals based monetary policy rule, which would be the optimal monetary policy without commitment when private agents have perfectly rational expectations, is unstable if in fact these agents follow standard adaptive learning rules. This Problem can be overcome if private expectations are observed and suitable incorporated into the policy maker's optimal rule. These strong results extend to the case in which there is simultaneous learning by the policy maker and the private agents. Our findings show the importance of conditioning policy appropriately, not just on fundamentals, but also directly on observed household and firm expectations.

expectations and the Stability Problem for optimal monetary policies
Research Papers in Economics, 2000CoAuthors: George W Evans, Seppo HonkapohjaAbstract:A fundamentals based monetary policy rule, which would be the optimal monetary policy without commitment when private agents have perfectly rational expectations, is unstable if in fact these agents follow standard adaptive learning rules. This Problem can be overcome if private expectations are observed and suitably incorporated into the policy maker's optimal rule. These strong results extend to the case in which there is simultaneous learning by the policy maker and the private agents. Our findings show the importance of conditioning policy appropriately, not just on fundamentals, but also directly on observed household and firm expectations.
John Michael Rassias  One of the best experts on this subject based on the ideXlab platform.

solution of the ulam Stability Problem for euler lagrange jensen k cubic mappings
Filomat, 2016CoAuthors: S A Mohiuddine, John Michael Rassias, Abdullah AlotaibiAbstract:The “oldest cubic” functional equation was introduced and solved by the second author of this paper (see: Glas. Mat. Ser. III 36(56) (2001), no. 1, 6372). which is of the form: f(x + 2y) = 3f(x + y) + f(x − y) − 3f(x) + 6f(y). For further research in various normed spaces, we are introducing new cubic functional equations, and establish fundamental formulas for the general solution of such functional equations and for the “Ulam Stability” of pertinent cubic functional inequalities.

generalized hyers ulam Stability for general additive functional equations in quasi β normed spaces
Journal of Mathematical Analysis and Applications, 2009CoAuthors: John Michael Rassias, Harkmahn KimAbstract:Abstract In 1940 S.M. Ulam proposed the famous Ulam Stability Problem. In 1941 D.H. Hyers solved the wellknown Ulam Stability Problem for additive mappings subject to the Hyers condition on approximately additive mappings. The first author of this paper investigated the Hyers–Ulam Stability of Cauchy and Jensen type additive mappings. In this paper we generalize results obtained for Jensen type mappings and establish new theorems about the Hyers–Ulam Stability for general additive functional equations in quasi β normed spaces.

generalization of ulam Stability Problem for euler lagrange quadratic mappings
Journal of Mathematical Analysis and Applications, 2007CoAuthors: John Michael RassiasAbstract:In 1968 S.M. Ulam proposed the Problem: “When is it true that by changing a little the hypotheses of a theorem one can still assert that the thesis of the theorem remains true or approximately true?” In 1978 P.M. Gruber proposed the Ulam type Problem: “Suppose a mathematical object satisfies a certain property approximately. Is it then possible to approximate this object by objects, satisfying the property exactly?” In this paper we solve the generalized Ulam Stability Problem for nonlinear Euler–Lagrange quadratic mappings satisfying approximately a mean equation and an Euler–Lagrange type functional equations in quasiBanach spaces and pBanach spaces.

Stability Problem of ulam for euler lagrange quadratic mappings
Journal of Inequalities and Applications, 2007CoAuthors: John Michael RassiasAbstract:We solve the generalized HyersUlam Stability Problem for multidimensional EulerLagrange quadratic mappings which extend the original EulerLagrange quadratic mappings.

Solution of the Ulam Stability Problem for quartic mappings
Glasnik Matematicki, 1999CoAuthors: John Michael RassiasAbstract:In 1940 S. M. Ulam proposed at the University of Wisconsin the Problem: "Give conditions in order for a linear mapping near an approximately linear mapping to exist." In 1968 S. Jvl. Ulam proposed the general Problem: "When is it true that by changing a little the hypotheses of a theorem one can still assert that the thesis of the theorem remains true or approximately true?" In 1978 P. 1\1. Gruber proposed the Ulam type Problem: "Suppose a mathematical object satisfies a certain property approximately. Is it then possible to approximate this object by objects, satisfying the property exactly?" According to P. lvl. Gruber this kind of Stability Problems is of particular interest in probability theory and in the case of functional equations of different types. In 19821998 we solved the above Ulam Problem, or equivalently the Ulam type Problem for linear mappings and also established analogous Stability Problems for quadratic and cubic mappings. In this paper we introduce the new quartic mappings F : X t Y , satisfying the new quartic functional equation F(XI + 2X2) + F(XI 2X2) + 6F(Xl) "" 4 [F(XI + X2) + F(XI X2) + 6F(X2)] for a1l2dimensional vectors (Xl,X2) E X2, with X a linear space (Y: "" a real complete linear space), and then solve the Ulam Stability Problem for the above mappings F. 1. QUARTIC FUNCTIONAL EQUATION DEFINITION 1.1. Let X be a linear space and let Y be a real complete linear space. Then a mapping F : X t Y, is called quartic, if the new quartic 1991 Mathematics Subject Classification. 39B.
Konstantin Turitsyn  One of the best experts on this subject based on the ideXlab platform.

inverse Stability Problem and applications to renewables integration
IEEE Control Systems Letters, 2018CoAuthors: Thanh Long Vu, Hung D Nguyen, Alexandre Megretski, Jeanjacques E Slotine, Konstantin TuritsynAbstract:In modern power systems, the operating point, at which the demand and supply are balanced, may take different values due to changes in loads and renewable generation levels. Understanding the dynamics of stressed power systems with a range of operating points would be essential to assuring their reliable operation, and possibly allow higher integration of renewable resources. This letter introduces a nontraditional way to think about the Stability assessment Problem of power systems. Instead of estimating the set of initial states leading to a given operating condition, we characterize the set of operating conditions that a power grid converges to from a given initial state under changes in power injections and lines. We term this Problem as “inverse Stability,” a Problem which is rarely addressed in the control and systems literature, and hence, poorly understood. Exploiting quadratic approximations of the system’s energy function, we introduce an estimate of the inverse Stability region. Also, we briefly describe three important applications of the inverse Stability notion: 1) robust Stability assessment of power systems with respect to different renewable generation levels; 2) Stabilityconstrained optimal power flow; and 3) Stabilityguaranteed corrective action design.

inverse Stability Problem and applications to renewables integration
arXiv: Systems and Control, 2017CoAuthors: Hung D Nguyen, Alexandre Megretski, Jeanjacques E Slotine, Konstantin TuritsynAbstract:In modern power systems, the operating point, at which the demand and supply are balanced, may take different values due to changes in loads and renewable generation levels. Understanding the dynamics of stressed power systems with a range of operating points would be essential to assuring their reliable operation, and possibly allow higher integration of renewable resources. This letter introduces a nontraditional way to think about the Stability assessment Problem of power systems. Instead of estimating the set of initial states leading to a given operating condition, we characterize the set of operating conditions that a power grid converges to from a given initial state under changes in power injections and lines. We term this Problem as "inverse Stability", a Problem which is rarely addressed in the control and systems literature, and hence, poorly understood. Exploiting quadratic approximations of the system's energy function, we introduce an estimate of the inverse Stability region. Also, we briefly describe three important applications of the inverse Stability notion: (i) robust Stability assessment of power systems w.r.t. different renewable generation levels, (ii) Stabilityconstrained optimal power flow (sOPF), and (iii) Stabilityguaranteed corrective action design.
Soonmo Jung  One of the best experts on this subject based on the ideXlab platform.

legendre s differential equation and its hyers ulam Stability
Abstract and Applied Analysis, 2007CoAuthors: Soonmo JungAbstract:We solve the nonhomogeneous Legendre's differential equation and apply this result to obtaining a partial solution to the HyersUlam Stability Problem for the Legendre's equation.