Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 16 of 16 for “"Stochastic differential equations (SDEs)"”.
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Strongly Asymptotically Optimal Methods for the Pathwise Global Approximation of Stochastic Differential Equations with Coefficients of Super-linear Growth
Our subject of study is strong approximation of stochastic differential equations (SDEs) with respect to the supremum and the L_p error criteria, and we seek approximations that are strongly asymptotically optimal in specific classes of approximations. For the supremum error, we prove strong …
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On optimal error rates for strong approximation of stochastic differential equations with irregular drift coefficients
… dissertation we study strong approximation of stochastic differential equations (SDEs) with irregular drift coefficients at the final time point or globally in time by methods that use only finitely many evaluations of the driving Brownian motion. We show the optimality of well-known methods, …
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No-Arbitrage Option Pricing with Neural SDEs
Neural stochastic differential equations (SDEs) represent a significant advancement in the field of machine learning by combining the power of neural networks and SDEs, two influential modelling approaches. SDEs are used to model systems that exhibit randomness or uncertainty and are defined by a …
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Statistical Inference for Stochastic Differential Equations using Splitting Schemes
… observed nonlinear first- and second-order stochastic differential equations (SDEs), focusing on splitting schemes and their applications. <br /> Initially, new numerical properties of splitting schemes, specifically the Lie-Trotter and Strang schemes, are established, enabling more accurate …
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Numerical approximation and parametric statistical inference of stochastic differential equations, with applications to finance
Stochastic differential equations (SDEs) have become an indispensable tool for modelling the dynamics of key state variables in mathematical finance such as instantaneous short rates of interest, share prices, and volatility processes. The appropriate application of SDEs requires reliable methods …
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Processing random signals in neuroscience, electrical engineering and operations research
… equation. Our mathematical models utilize stochastic differential equations (SDEs) and stochastic optimal control, both of which were born in the soil of electrical engineering. Central to this dissertation is a brain-physics based model of cerebrospinal fluid (CSF) dynamics, whose …
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Parameter Estimation Techniques for Nonlinear Dynamic Models with Limited Data, Process Disturbances and Modeling Errors
… are proposed for estimating parameters in Stochastic Differential Equations (SDEs). SDEs are fundamental dynamic models that take into account process disturbances and model mismatch. Three new approximate maximum likelihood methods are developed for estimating parameters in SDE models. …
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Identifying and Characterizing Transition Cells in Developmental Processes from scRNA-Seq Data
… as a function of gene regulatory relations using stochastic differential equations (SDEs). Based on dynamical systems theory, I developed a statistical approach, CellTran, which leverages pairwise gene expression correlation coefficients to infer cell state transitions. I validated this method …
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Inference for auto-regulatory genetic networks using diffusion process approximations
… study the applicability of the EA methodology to Stochastic Differential Equations (SDEs) which approximate biological systems. In principle EA can be applied to any scalar-valued SDE as long as a transformation (known as Lamperti transform) exists that sets the (new) infinitesimal variance to …
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Stochastic Algorithms in Riemannian Manifolds and Adaptive Networks
… combination of adaptive network algorithms and stochastic geometric dynamics has the potential to make a large impact in distributed control and signal processing applications. However, both literatures contain fundamental unsolved problems. The thesis is thus in two main parts. In part I, we …
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The stochastic modelling of the neuronal membrane potential in response to synaptic input
… of the solution of a family of three linked stochastic differential equations (SDEs). In this thesis it is demonstrated that the conclusion of the lengthy analysis of Rudolph and Destexhe (2003, 2005) can be obtained directly from the system of SDEs. Through the use of a spectral procedure …
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Efficient Sampling Methods of, by, and for Stochastic Dynamical Systems
… statistics and computational dynamics. Stochastic differential equations (SDEs) are used to model a variety of physical systems, and computing expectations over marginal distributions of SDEs is important for the analysis of such systems. In particular, quantifying the probabilities of …
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Principled Methods for Advancing Generative Machine Learning
… its underlying causes and propose a new class of stochastic differential equations (SDEs) — risk-sensitive SDEs — as the backbone of continuous-time diffusion models. This approach is principled and accommodates various noise assumptions. Another example explored in this thesis concerns neural …
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Statistical Inference and Learning for Stochastic and Partial Differential Equations
Learning differential equation models from data is of significant interest to the scientific and engineering communities. Fundamental to many areas of science, differential equations are the mathematical description of change, derived from physical laws and modelling assumptions. Practically, …
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Stochastic Mean Field Games within Complex Systems and Interacting Particle Frameworks
… aims to analyze several advanced topics in stochastic analysis. We begin by examining diffusion approximations for transport equations with dissipative drifts, addressing both time-dependent and time-independent cases. We establish results on the existence and uniqueness of solutions for …
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Computational Techniques for the Analysis of Large Scale Biological Systems
… yellow fever mosquito. Cell cycle system evolves stochastic effects when there are a small number of molecules react each other. Consequently, the stochastic effects of the cell cycle are important, and the evolution of cells is best described statistically. Stochastic simulation algorithm (SSA), …