Lévy Processes—From Probability to Finance and Quantum Groups

By David Applebaum. 2004

486 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/876a3d5194a408f05e0540bacba044ab193e7d11

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Citations in the corpus

Recent progress in coalescent theory (2009, unknown): “(I learnt of this in a short but very informative account [7]).”
A Nonhomogeneous Fractional p-Kirchhoff Type Problem Involving Critical Exponent in ℝN (2016, background): “Indeed, this type of operator arises in a quite natural way in many different applications such as continuum mechanics, phase transition phenomena, population dynamics, minimal surfaces and game theory; see for example [4, 12, 15, 23] and the references therein.”
The Brezis–Nirenberg type problem involving the square root of the Laplacian (2011, background): “These processes have been applied to American options in mathematical finance for modelling the jump processes of the financial derivatives such as futures, forwards, options, and swaps, see [2] and references therein.”
Fractional Kirchhoff problems with critical Trudinger–Moser nonlinearity (2019, background): “1) are important in many fields of science, notably continuum mechanics, phase transition phenomena, population dynamics, minimal surfaces and anomalous diffusion, as they are the typical outcome of stochastically stabilization of Lévy processes, see [1,4,21] and the references therein.”
Existence and multiplicity of entire solutions for fractional p-Kirchhoff equations (2016, background): “This type of operators arises in a quite natural way in many di erent applications, such as, continuummechanics, phase transition phenomena, population dynamics and game theory, as they are the typical outcome of stochastically stabilization of Lévy processes, see for instance [3, 9, 10] and the ref”
Fractional elliptic equations with critical exponential nonlinearity (2016, background): “Fractional operators are involved in financial mathematics, where Lévy processes with jumps appear in modeling the asset prices (see [5]).”
Positive solutions of nonlinear problems involving the square root of the Laplacian (2009, methodology): “Lévy processes have also been applied to model American options [2].”
Nonlocal Kirchhoff Problems with Singular Exponential Nonlinearity (2020, background): “Moreover, such equations and the associated fractional operators allow us to develop a generalization of quantum mechanics and also to describe the motion of a chain or an array of particles that are connected by elastic springs as well as unusual diffusion processes in turbulent fluid motions and m”
Fractional diffusion with Neumann boundary conditions: the logistic equation (2012, background): “1 Introduction Nonlocal operators, and notably fractional ones, are a classical topic in harmonic analysis and operator theory, and they are recently becoming impressively popular because of their connection with many real-world phenomena, from physics [20, 14, 21] to mathematical nonlinear analysis”
Asymptotics for Exponential Levy Processes and Their Volatility Smile: Survey and New Results (2012, unknown): “, [41], [17], [101], [13], [24], [111], [7], [34], to mention just a few.”