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You searched for subject:(Reflected diffusions). Showing records 1 – 2 of 2 total matches.

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University of Kansas

1. Han, Zheng. Reflected diffusions and applications to finance and operations management.

Degree: PhD, Mathematics, 2015, University of Kansas

This dissertation provides explicit solutions to four special stochastic optimal control problems for reflected diffusions and Markov modulated reflected diffusions. The main mathematical tool that we use is the ergodic theory for stochastic differential equations (SDE’s), in particular, the ergodic theory for reflected diffusions. First, we present some basic definitions of reflected diffusions, the Itô’s formulas. After this we study the ergodic theorems, namely, the law of large numbers, for reflected diffusions. The reflected diffusions and Markov modulated reflected diffusions are used to simulate bounded price dynamics regulated by policy makers. Motivated by this, we analyze several stochastic optimal control problems for reflected diffusions (or for Markov modulated reflected diffusions). These stochastic optimal control problems are solved in the sense that we can reduce them to some explicit optimization problems. Numerical computations are also given for the reduced optimization problems. Our work resulted in one accepted paper, one completed paper and two on-going projects. Advisors/Committee Members: Hu, Yaozhong (advisor), Nualart, David (cmtemember), Liu, Weishi (cmtemember), Tu, Xuemin (cmtemember), Zhang, Jianbo (cmtemember).

Subjects/Keywords: Mathematics; Finance; Operations research; Ergodic theory; Optimal barrier; Reflected diffusions

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APA (6th Edition):

Han, Z. (2015). Reflected diffusions and applications to finance and operations management. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/21698

Chicago Manual of Style (16th Edition):

Han, Zheng. “Reflected diffusions and applications to finance and operations management.” 2015. Doctoral Dissertation, University of Kansas. Accessed October 23, 2017. http://hdl.handle.net/1808/21698.

MLA Handbook (7th Edition):

Han, Zheng. “Reflected diffusions and applications to finance and operations management.” 2015. Web. 23 Oct 2017.

Vancouver:

Han Z. Reflected diffusions and applications to finance and operations management. [Internet] [Doctoral dissertation]. University of Kansas; 2015. [cited 2017 Oct 23]. Available from: http://hdl.handle.net/1808/21698.

Council of Science Editors:

Han Z. Reflected diffusions and applications to finance and operations management. [Doctoral Dissertation]. University of Kansas; 2015. Available from: http://hdl.handle.net/1808/21698

2. Fan, Wai Tong. Interacting particle systems with partial annihilation through membranes.

Degree: PhD, 2014, University of Washington

This thesis studies the hydrodynamic limit and the fluctuation limit for a class of interacting particle systems in domains. These systems are introduced to model the transport of positive and negative charges in solar cells. However, they are general microscopic models that can describe a variety of macroscopic phenomena with coupled boundary conditions, such as the population dynamics of two segregated species under competition. Proving these two types of limits represents establishing the functional law of large numbers and the functional central limit theorem, respectively, for the time-trajectory of the particle densities. This also corresponds to the study of the behavior of the system at two different scales. We show that the hydrodynamic limit is a pair of deterministic measures whose densities solve a coupled nonlinear heat equations, while the fluctuation limit can be described by a Gaussian Markov process that solves a stochastic partial differential equation. Advisors/Committee Members: Chen, Zhen-Qing (advisor).

Subjects/Keywords: Fluctuations; Hydrodynamic limits; Interacting particle systems; Reflected diffusions; Stochastic processes; Mathematics; mathematics

…state space of (XN,+ , XN,− )t≥0 t t empirical measure for reflected diffusions… …reflected Brownian motions (or more generally, reflected diffusions) with drift on D… …particles perform reflected diffusions on continuous state spaces rather than random 8 walks… …details about reflected diffusions. We now describe the annihilating diffusion model. Heuristic… …system of reflected diffusions. Fluctuations of the reaction-diffusion systems on the cube… 

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Fan, W. T. (2014). Interacting particle systems with partial annihilation through membranes. (Doctoral Dissertation). University of Washington. Retrieved from http://hdl.handle.net/1773/26532

Chicago Manual of Style (16th Edition):

Fan, Wai Tong. “Interacting particle systems with partial annihilation through membranes.” 2014. Doctoral Dissertation, University of Washington. Accessed October 23, 2017. http://hdl.handle.net/1773/26532.

MLA Handbook (7th Edition):

Fan, Wai Tong. “Interacting particle systems with partial annihilation through membranes.” 2014. Web. 23 Oct 2017.

Vancouver:

Fan WT. Interacting particle systems with partial annihilation through membranes. [Internet] [Doctoral dissertation]. University of Washington; 2014. [cited 2017 Oct 23]. Available from: http://hdl.handle.net/1773/26532.

Council of Science Editors:

Fan WT. Interacting particle systems with partial annihilation through membranes. [Doctoral Dissertation]. University of Washington; 2014. Available from: http://hdl.handle.net/1773/26532

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