Stochastic Control of Hereditary Systems and Applications

doi:10.1007/978-0-387-75816-9

Stochastic Modelling and Applied Probability

2008

DOI: 10.1007/978-0-387-75816-9

|View full text |Cite

Stochastic Control of Hereditary Systems and Applications

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2015

2022

Publication Types

Select...

Article4

Relationship

Self Cite0

Independent4

Authors

Journals

Cited by 4 publications

References 76 publications

(143 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

Optimal Control for Stochastic Delay Evolution Equations

Meng

Shen

2015

Appl Math Optim

View full text Add to dashboard Cite

In this paper, we investigate a class of infinite-dimensional optimal control problems, where the state equation is given by a stochastic delay evolution equation with random coefficients, and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation. We first prove the continuous dependence theorems for stochastic delay evolution equations and anticipated backward stochastic evolution equations, and show the existence and uniqueness of solutions to anticipated backward stochastic evolution equations. Then we establish necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin's maximum principles. To illustrate the theoretical results, we apply stochastic maximum principles to study two examples, an infinite-dimensional linearquadratic control problem with delay and an optimal control of a Dirichlet problem for a stochastic partial differential equation with delay. Further applications of the two examples to a Cauchy problem for a controlled linear stochastic partial differential equation and an optimal harvesting problem are also considered.

show abstract

Optimal Control for Stochastic Delay Evolution Equations

Meng

Shen

2015

Appl Math Optim

View full text Add to dashboard Cite

show abstract

Optimal relaxed control of stochastic hereditary evolution equations with Lévy noise

Manna

Mukherjee

2019

ESAIM: COCV

View full text Add to dashboard Cite

Existence theory of optimal relaxed control problem for a class of stochastic hereditary evolution equations driven by Lévy noise has been studied. We formulate the problem in the martingale sense of Stroock and Varadhan to establish existence of optimal controls. The construction of the solution is based on the classical Faedo–Galerkin approximation, the compactness method and the Jakubowski version of the Skorokhod theorem for nonmetric spaces, and certain compactness properties of the class of Young measures on Suslin metrizable control sets. As application of the abstract theory, Oldroyd and Jeffreys fluids have been studied and existence of optimal relaxed control is established. Existence and uniqueness of a strong solution and uniqueness in law for the two-dimensional Oldroyd and Jeffreys fluids are also shown.

show abstract

Compensating Operator and Weak Convergence of Semi-Markov Process to the Diffusion Process without Balance Condition

Malyk

2015

Journal of Applied Mathematics

View full text Add to dashboard Cite

Weak convergence of semi-Markov processes in the diffusive approximation scheme is studied in the paper. This problem is not new and it is studied in many papers, using convergence of random processes. Unlike other studies, we used in this paper concept of the compensating operator. It enables getting sufficient conditions of weak convergence under the conditions on the local characteristics of output semi-Markov process.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Stochastic Control of Hereditary Systems and Applications

Cited by 4 publications

References 76 publications

Optimal Control for Stochastic Delay Evolution Equations

Optimal Control for Stochastic Delay Evolution Equations

Optimal relaxed control of stochastic hereditary evolution equations with Lévy noise

Compensating Operator and Weak Convergence of Semi-Markov Process to the Diffusion Process without Balance Condition

Contact Info

Product

Resources

About