Titlebook: Numerical Probability; An Introduction with Gilles Pagès Textbook 2018 Springer Nature Switzerland AG 2018 Monte Carlo method.variance redu

硬化

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Trigger-Point

https://doi.org/10.1007/978-3-319-90276-0Monte Carlo method; variance reduction; Quasi-Monte Carlo method; stochastic differential equation disc

尾隨

ologie gestattet es, zahlreiche und auf den ersten Blick sehr unterschiedliche Probleme bündig und einheitlich zu formulieren und sie einer gemeinsamen anschaulichen Vorstellung zu unterwerfen. Zur anschlie?enden . dieser Probleme tr?gt die Mengentheoretische Topologie im engeren Sinne ziemlich weni

手段

Simulation of Random Variables,of pseudorandom numbers, the inverse distribution function method and von Neumann’s acceptance-rejection method, with applications to the simulation of Gaussian vectors, (fractional) Brownian motion and Poisson process paths.

流逝

The Monte Carlo Method and Applications to Option Pricing, Law of Large Numbers (without proof) and the different ways to measure its rate of convergence (quadratic mean, Central Limit theorem, Law of the Iterated Logarithm), we introduce the notion of confidence interval at a given confidence level, illustrated by a simple application to the pricing of a

Inflammation

Variance Reduction, by replacing the random variable of interest by another one with the same expectation but lower variance. This chapter presents the main methods to do so: static and dynamic (regression) control variate, convexity methods (Jensen’s inequality), antithetic method, pre-conditioning (Blackwell-Rao), s

植物群

The Quasi-Monte Carlo Method,-random numbers are replaced by deterministic computable sequences of .-valued vectors which, once substituted . in place of pseudo-random numbers in the Monte Carlo method, may significantly speed up its rate of convergence, making it . independent of the structural dimension . of the simulation.

monologue

degradation

Stochastic Approximation with Applications to Finance,ep Learning applications. We show when and how to design a stochastic gradient or a zero search recursive stochastic algorithm. We prove the main convergence theorems (.... and in quadratic mean) as well as their rates of convergence (Central Limit theorem). The Ruppert & Polyak averaging procedure,

single

Discretization Scheme(s) of a Brownian Diffusion,the (discrete time and continuous) Euler scheme and the Milstein scheme. The existence of moments, the strong (or pathwise) convergence rate in . (and a:s:) of both schemes are established under Lipschitz assumptions of the diffusion coeffcients (Euler scheme) or of their partial derivatives (Milste