A Characterization of the Existence of Solutions for Hamilton—Jacobi Equations in Ergodic Control Problems with Applications

2000 ◽  
Vol 42 (1) ◽  
pp. 35-50 ◽  
Author(s):  
M. Arisawa
Keyword(s):  
Existence Of Solutions ◽  
Control Problems ◽  
Ergodic Control ◽  
Jacobi Equations

scholarly journals Ergodic control of diffusions with random intervention times

2021 ◽  
Vol 58 (1) ◽  
pp. 1-21
Author(s):  
Harto Saarinen ◽  
Jukka Lempa
Keyword(s):  
Optimal Solution ◽  
Singular Control ◽  
Control Policy ◽  
Control Problems ◽  
Ergodic Control ◽  
Linear Diffusion ◽  
One Dimensional ◽  
And Diffusion ◽  
Independent Poisson Process ◽  
Exact Amount

AbstractWe study an ergodic singular control problem with constraint of a regular one-dimensional linear diffusion. The constraint allows the agent to control the diffusion only at the jump times of an independent Poisson process. Under relatively weak assumptions, we characterize the optimal solution as an impulse-type control policy, where it is optimal to exert the exact amount of control needed to push the process to a unique threshold. Moreover, we discuss the connection of the present problem to ergodic singular control problems, and illustrate the results with different well-known cost and diffusion structures.

scholarly journals Existence and Characterization of Solutions of Nonlinear Volterra-Stieltjes Integral Equations in Two Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Mohamed Abdalla Darwish ◽  
Józef Banaś
Keyword(s):  
Integral Equations ◽  
Nonlinear Integral Equation ◽  
Existence Of Solutions ◽  
Stieltjes Integral ◽  
Basic Tool ◽  
Measures Of Noncompactness ◽  
Characterization Of Solutions ◽  
Fractional Orders ◽  
Stieltjes Type

The paper is devoted mainly to the study of the existence of solutions depending on two variables of a nonlinear integral equation of Volterra-Stieltjes type. The basic tool used in investigations is the technique of measures of noncompactness and Darbo’s fixed point theorem. The results obtained in the paper are applicable, in a particular case, to the nonlinear partial integral equations of fractional orders.

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