The First Attempt on the Stochastic Calculus on Time Scale

Du, Nguyen Huu; Dieu, Nguyen Thanh

doi:10.1080/07362994.2011.610169

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Introduction4

Theorem 9 Suppose Is Rd-continuous and Regressive And Let1

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Cited by 14 publications

(9 citation statements)

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“…Time scales were first introduced by Hilger [4] in 1988 in order to unite and extend the continuous and discrete analysis into a general framework. Time scales theory has been extensively studied in many works [5][6][7][8][9][10]. It is well known that the optimal control problem on time scales is an important field for both theory and applications.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Linear Quadratic Control Problem on Time Scales

Zhu

Jia

2021

Discrete Dynamics in Nature and Society

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This paper addresses a version of the stochastic linear quadratic control problem on time scales S Δ LQ , which includes the discrete time and continuous time as special cases. Riccati equations on time scales are given, and the optimal control can be expressed as a linear state feedback. Furthermore, we present the uniqueness and existence of the solution to the Riccati equation on time scales. Furthermore, we give an example to illustrate the theoretical results.

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Section: Introductionmentioning

confidence: 99%

Stochastic Linear Quadratic Control Problem on Time Scales

Zhu

Jia

2021

Discrete Dynamics in Nature and Society

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“…Recently, work has begun on extending stochastic calculus to time scales, for example, [58] for the isolated time scale case, [59,60] for the delta case, AND [61] for the nabla case.…”

Section: Theorem 9 Suppose Is Rd-continuous and Regressive And Letmentioning

confidence: 99%

A Survey of Recent Results for the Generalizations of Ordinary Differential Equations

Biles

Federson

Pouso

2014

Abstract and Applied Analysis

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“…is allows us to deal with the continuous and discrete analyses from the common point of view. Recently, time scale theory is extensively studied in many works [8][9][10][11][12][13]. It is well known that the optimal control problems on time scales are an important field for both theory and applications.…”

Section: Introductionmentioning

confidence: 99%