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# Browsing Auburn Theses and Dissertations by Author "Nane, Erkan"

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### Applications of Stochastic Gradient Descent for Optimization of Complex Systems with Uncertainty

Das, Somak (2021-07-27)

The Stochastic Gradient Descent (SGD) method in all its variations has gained popularity with the recent progress in Machine learning. In this dissertation we implement and analyze two modifications of the SGD method. In ...

### Intermittency properties of space-time fractional stochastic partial differential equations

Asogwa, Sunday (2019-07-11)

This dissertation focuses on the analyses of the non-linear time-fractional stochastic reaction-diffusion equations of the type
\begin{equation}\label{abstract-eq}
\partial^\beta_tu_t(x)=-\nu(-\Delta)^{\alpha/2} ...

### Phase transition for fractional stochastic partial differential equations in a bounded domain

Guerngar, Ngartelbaye (2019-07-18)

In this dissertation, we study several stochastic partial differential equations (SPDEs) in the open and bounded domain $D$, subset of $\mathbb{R}^d$ for $d\geq 1$, driven by a multiplicative noise. We are interested in ...

### Solvability and exact moment asymptotics for the interpolated stochastic heat and wave equation and the existence of an invariant measure for a special case.

Eisenberg, Nicholas (2022-08-05)

This thesis will consist of two main projects, Chapters 2 and 4, and a smaller project in Chapter 3. We will be studying a general space-time fractional stochastic partial differential equation in Chapters 2 and 3 and the ...

### Space-Time Fractional Cauchy Problems and Trace Estimates for Relativistic Stable Processes

Mijena, Jebessa (2013-07-16)

Fractional derivatives can be used to model time delays in a diffusion process. When the order of the fractional derivative is distributed over the unit interval, it is useful for modeling a mixture of delay sources. In ...

### A Study of Space-time Fractional SPDE in Bounded Domains

Negash, Alemayehu (2023-07-24) ETD File Embargoed

This dissertation considers space-time fractional stochastic heat equation on a regular bounded domain B in R^d, d ⩾ 1 with Dirichlet boundary condition:
∂βt ut(x) = −(−Δ)α2 ut(x) + I1−βt [λσ(ut(x)) ˙W (t, x)] for x ∈ B ...

### Study of Stochastic Differential Equation Driven by Time-Changed Levy Noise

Ni, Yinan (2020-03-24)

This dissertation is composed of two parts. The first part studies stabilities of the solution
of stochastic differential equation (SDE) driven by time-changed L´evy noise in probability,
moment, and path sense. This ...