scholarly journals Recovery of piecewise constant coefficients in optical diffusion tomography

2000 ◽  
Vol 7 (13) ◽  
pp. 468 ◽  
Author(s):  
V. Kolehmainen ◽  
M. Vauhkonen ◽  
J. P. Kaipio ◽  
S. R. Arridge
Keyword(s):  
Piecewise Constant ◽  
Constant Coefficients ◽  
Optical Diffusion Tomography

scholarly journals Fractional stochastic heat equation with piecewise constant coefficients

2020 ◽  
Vol 21 (01) ◽  
pp. 2150002
Author(s):  
Yuliya Mishura ◽  
Kostiantyn Ralchenko ◽  
Mounir Zili ◽  
Eya Zougar
Keyword(s):  
Diffusion Coefficient ◽  
Heat Equation ◽  
Divergence Form ◽  
Stochastic Heat Equation ◽  
Piecewise Constant ◽  
Constant Diffusion Coefficient ◽  
Infinite Dimensional ◽  
Order Elliptic Operator ◽  
Constant Diffusion ◽  
Constant Coefficients

We introduce a fractional stochastic heat equation with second-order elliptic operator in divergence form, having a piecewise constant diffusion coefficient, and driven by an infinite-dimensional fractional Brownian motion. We characterize the fundamental solution of its deterministic part, and prove the existence and the uniqueness of its solution.

scholarly journals A weak convergence approach to hybrid LQG problems with infinite control weights

2002 ◽  
Vol 15 (1) ◽  
pp. 1-21
Author(s):  
G. George Yin ◽  
Jiongmin Yong
Keyword(s):  
Markov Chain ◽  
Weak Convergence ◽  
Small Parameter ◽  
Limit Problem ◽  
Discrete Events ◽  
Linear Quadratic ◽  
Piecewise Constant ◽  
Constant Coefficients ◽  
The Cost ◽  
Random Times

This work is concerned with a class of hybrid LQG (linear quadratic Gaussian) regulator problems modulated by continuous-time Markov chains. In contrast to the traditional LQG models, the systems have both continuous dynamics and discrete events. In lieu of a model with constant coefficients, these coefficients vary with time and exhibit piecewise constant behavior. At any time t, the system follows a stochastic differential equation in which the coefficients take one of the m possible configurations where m is usually large. The system may jump to any of the possible configurations at random times. Further, the control weight in the cost functional is allowed to be indefinite. To reduce the complexity, the Markov chain is formulated as singularly perturbed with a small parameter. Our effort is devoted to solving the limit problem when the small parameter tends to zero via the framework of weak convergence. Although the limit system is still modulated by a Markov chain, it has a much smaller state space and thus, much reduced complexity.

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