Titlebook: Heat Kernel Method and its Applications; Ivan Avramidi Book 2015 Springer International Publishing Switzerland 2015 heat kernel.heat equat

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Introduction to Differential GeometryIn this chapter we give a brief introduction to basic concepts of differential geometry. This is a huge subject and we will only introduce background material necessary for the study of the heat kernel on Riemannian manifolds. A wide range of books on differential geometry at various levels of difficulty is listed in the bibliography.

CAB

Singular PerturbationsIn this chapter we introduce the basic principles of the singular perturbation techniques to study the semiclassical asymptotics and apply them to obtain the asymptotic expansion of the heat equation.

抛射物

Stochastic ProcessesIn this chapter we introduce the basic concepts of probability and stochastic processes such as Wiener process and Poisson process. Next, we present some basic concepts of stochastic calculus and discuss stochastic differential equations, in particular, such fundamental topics as Itô’s Lemma and forward and backward Kolmogorov equations.

情爱

Applications in Mathematical FinanceThis chapter presents an introduction to mathematical finance. After a short review of financial instruments we introduce various models, including, Black-Scholes model, stochastic volatility models and jump diffusion models, and apply the methods described in previous chapters to SABR model and Heston model.

surrogate

CULP

LOPE

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Accolade

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