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Integral equations. --- Boundary value problems. --- Differential equations --- Mathematical physics

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Stochastic processes --- Mathematical potential theory --- 517.9 --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis

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Lévy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. Here, the author ties these two subjects together, beginning with an introduction to the general theory of Lévy processes, then leading on to develop the stochastic calculus for Lévy processes in a direct and accessible way. This fully revised edition now features a number of new topics. These include: regular variation and subexponential distributions; necessary and sufficient conditions for Lévy processes to have finite moments; characterisation of Lévy processes with finite variation; Kunita's estimates for moments of Lévy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Lévy processes; multiple Wiener-Lévy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Lévy-driven SDEs.

Lévy processes --- Stochastic analysis --- Lévy, Processus de --- Analyse stochastique --- Lévy processes. --- Stochastic analysis. --- Lévy processes --- Lévy, Processus de --- Lévy processes. --- Stochastic integral equations. --- Integral equations --- Random walks (Mathematics) --- Analysis, Stochastic --- Mathematical analysis --- Stochastic processes

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Scattering theory is, roughly speaking, perturbation theory of self-adjoint operators on the (absolutely) continuous spectrum. It has its origin in mathematical problems of quantum mechanics and is intimately related to the theory of partial differential equations. Some recently solved problems, such as asymptotic completeness for the Schrödinger operator with long-range and multiparticle potentials, as well as open problems, are discussed. Potentials for which asymptotic completeness is violated are also constructed. This corresponds to a new class of asymptotic solutions of the time-dependent Schrödinger equation. Special attention is paid to the properties of the scattering matrix, which is the main observable of the theory. The book is addressed to readers interested in a deeper study of the subject.

Operator theory --- Scattering (Mathematics) --- Mathematical Theory --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Mathematical analysis. --- Analysis (Mathematics). --- Functional analysis. --- Integral equations. --- Partial differential equations. --- Mathematical physics. --- Analysis. --- Functional Analysis. --- Integral Equations. --- Partial Differential Equations. --- Theoretical, Mathematical and Computational Physics. --- Physical mathematics --- Physics --- Partial differential equations --- Equations, Integral --- Functional equations --- Functional analysis --- Functional calculus --- Calculus of variations --- Integral equations --- 517.1 Mathematical analysis --- Mathematical analysis

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Nonlinearity & Functional Analysis

Functional analysis --- Mathematical analysis. --- Functional analysis. --- Nonlinear theories. --- Mathematical analysis --- Nonlinear theories --- Analyse mathématique --- Analyse fonctionnelle --- Théories non linéaires --- ELSEVIER-B EPUB-LIV-FT --- 517.1 --- 517.9 --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Nonlinear problems --- Nonlinearity (Mathematics) --- Calculus --- Mathematical physics --- 517.1 Mathematical analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations