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tfg_jordi_petchame_guerrero.pdf (933.41 KB)

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Bachelor thesis

Publication date

2021-01-24

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cc-by-nc-nd (c) Jordi Petchamé Guerrero, 2021
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/181532

From the classical to the stochastic heat equation

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[en] This bachelor’s thesis revolves around the connection between stochastic processes and the heat equation. The main goal is to carry out a thorough study of the transition from the classical to the stochastic one-dimensional heat equation. In order to develop the mathematical framework for linear stochastic partial differential equations, we use tools of basic probability theory, calculus and functional analysis. We start with a concise study of the classical deterministic heat equation, from its physical derivation to the search for explicit solutions under specific conditions. Then, we describe the mathematical foundations of the stochastic version of this partial differential equation, focusing on Gaussian stochastic processes. On that basis, we define the stochastic heat equation on $\mathbb{R}$. Finally, we conclude this project with a comprehensive analysis of its solutions’ continuity properties.

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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Marta Sanz

Subject

Equació de la calor, Treballs de fi de grau, Equacions en derivades parcials, Processos gaussians, Anàlisi estocàstica

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Heat equation, Bachelor's theses, Partial differential equations, Gaussian processes, Stochastic analysis

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

PETCHAMÉ GUERRERO, Jordi. From the classical to the stochastic heat equation. [consulted: 9 of August of 2026]. Available at: https://hdl.handle.net/2445/181532

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