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- W2322275787 abstract "Following [FdVOPS01], we study a stochastic Landau-Ginzburg differential equation of the form d' = A'+ d⌘(t, ~x), where A is a function defined on the space of random variables (x, t), with (x, t) 2 R⇥Zd. Using the stochastic analysis theory (more precisely, the Feynman-Kac formula) we are able to associate this stochastic differential equation (EDE) with an evolution equation. In this way, our study is resumed to the problem of determine the spectrum of the generator of an evolution semigroup. To do this, we use techniques developed in the quantum field theory. This work is organized as follows. In the Introduction we formulate our problem in detail, providing the aspects of the stochastic analysis and field theory that are involved. We also enunciate a theorem that resumes the spectral properties that we want to achieve. Chapters 2 and 3 are meant to provide the conceptual tools that are needed to the development of the initial problem. Yet in Chapter 3, we do a quick review of a known problem in quantum field (the model '), intending estabilish familiarity with this theory. Chapter 4 is restricted initially to the determination of spectral properties of our problem in the finite volume [ T, T ] ⇥ ⇤ ⇢ R ⇥ Z, and then we perform the cluster expansion in order to formulate the problem in infinite volume [ T, T ]⇥ Z. In Chapter 5 we define the Bethe-Salpeter operator and, in Chapter 6, we determine some properties of the kernel of this operator. This informations are used in Chapter 7 to obtain the desired spectral characterization." @default.
- W2322275787 created "2016-06-24" @default.
- W2322275787 creator A5066203514 @default.
- W2322275787 date "2017-06-20" @default.
- W2322275787 modified "2023-10-05" @default.
- W2322275787 title "Espectro de geradores de dinâmica em EDPs estocásticas" @default.
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- W2322275787 doi "https://doi.org/10.11606/d.55.2016.tde-31032016-105652" @default.
- W2322275787 hasPublicationYear "2017" @default.
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