Linear Functional Differential Equations as Semigroups on Product Spaces

Burns, John A.; Herdman, Terry L.; Stech, Harlan W.

doi:10.1137/0514007

Cited by 114 publications

(99 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…M 2 will be the ambient space where setting our problem. It can be proved (see Burns et al (1983) Theorem 2.3, page 102) that the operator…”

Section: Discussionmentioning

confidence: 99%

“…In the new (infinite dimensional) state equation (that is (33)) the lags in time disappear and the state equation reads as a standard stochastic evolution equation in the infinite dimensional space. To perform this first step we use first the results of Burns et al (1983) and Kappel and Zhang (1986) for deterministic NDE (Appendix A.2) and then we introduce the noise (Appendix A.3).…”

Section: Discussionmentioning

confidence: 99%

“…If P is in L 2 loc [0, +∞) (see Burns et al (1983), page 109) such an NDE has a unique (generalized in the sense of Kappel and Zhang (1986)…”

Section: Chosen (X Imentioning

confidence: 99%

See 2 more Smart Citations

International borrowing without commitment and informational lags: Choice under uncertainty

Fabbri

2017

Journal of Mathematical Economics

View full text Add to dashboard Cite

Abstract. A series of recent studies in economic growth theory have considered a class of models of international borrowing where, in the absence of a perfect investment commitment, the borrowing constraint depends on the historical performances of the country. Thus, a better level of past economic activity gives a higher reputation, thereby increasing the possibility of accessing the international credit market. This note considers this problem in a stochastic setting based on the volatility of the internal net capital. We study how the optimal consumption level and the maximal expected welfare depend on the combined influence of the trajectory of past economic variables and the volatile environment. In particular, we show how the strength of the history effect and the relative weight of the historical performance depend on the degree of risk.

show abstract

“…M 2 will be the ambient space where setting our problem. It can be proved (see Burns et al (1983) Theorem 2.3, page 102) that the operator…”

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

International borrowing without commitment and informational lags: Choice under uncertainty

Fabbri

2017

Journal of Mathematical Economics

View full text Add to dashboard Cite

show abstract

“…Later we shall return to this issue from an operator point of view. Let us consider know the operator model of the system (3) used in [18] (see also [2]):ẋ…”

Section: The Neutral Type System and The Infinite Dimensional Modelmentioning

confidence: 99%

“…where This model was used in particular in [18] for the analysis of the stability of the system (2) and in [15] for the analysis of the controllability problems (see also [2,10]). From the operator point of view, the regular feedback law (4) means a perturbation of the infinitesimal generator A by the operator BF which is relatively A-bounded (cf.…”

Section: The Neutral Type System and The Infinite Dimensional Modelmentioning

confidence: 99%

On Pole Assignment and Stabilizability of Neutral Type Systems

Rabah

Sklyar

Rezounenko

2009

Topics in Time Delay Systems

View full text Add to dashboard Cite

Summary. In this note we present a systematic approach to the stabilizability problem of linear infinite-dimensional dynamical systems whose infinitesimal generator has an infinite number of instable eigenvalues. We are interested in strong non-exponential stabilizability by a linear feed-back control. The study is based on our recent results on the Riesz basis property and a careful selection of the control laws which preserve this property. The investigation may be applied to wave equations and neutral type delay equations.

show abstract

On the optimal control of a linear neutral differential equation arising in economics

Boucekkine

Fabbri

Pintus

2011

Optim Control Appl Methods

View full text Add to dashboard Cite

SUMMARYIn this paper, we apply two optimization methods to solve an optimal control problem of a linear neutral differential equation (NDE) arising in economics. The first one is a variational method, and the second follows a dynamic programming approach. Because of the infinite dimensionality of the NDE, the second method requires the reformulation of the latter as an ordinary differential equation in an appropriate abstract space. It is shown that the resulting Hamilton-Jacobi-Bellman equation admits a closed-form solution, allowing for a much finer characterization of the optimal dynamics compared with the alternative variational method. The latter is clearly limited by the nontrivial nature of asymptotic analysis of NDEs. Copyright

show abstract

Linear Functional Differential Equations as Semigroups on Product Spaces

Cited by 114 publications

References 17 publications

International borrowing without commitment and informational lags: Choice under uncertainty

International borrowing without commitment and informational lags: Choice under uncertainty

On Pole Assignment and Stabilizability of Neutral Type Systems

On the optimal control of a linear neutral differential equation arising in economics

Contact Info

Product

Resources

About