By Harald Niederreiter, Denis Talay
This e-book represents the refereed lawsuits of the 6th foreign convention on Monte Carlo and Quasi-Monte Carlo equipment in medical Computing and of the second one overseas convention on Monte Carlo and Probabilistic tools for Partial Differential Equations. those meetings have been held together at Juan-les-Pins (France) in June 2004. The lawsuits comprise conscientiously chosen papers on many facets of Monte Carlo tools, quasi-Monte Carlo tools, and the numerical resolution of partial differential equations. The reader may be knowledgeable approximately present study in those very lively parts.
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Additional info for Monte Carlo and Quasi-Monte Carlo Methods 2004
Example text
NCCR-FINRISK Working Paper Series 253, 2005. php [Kar03] I. Karatzas. A note on Bayesian detection of change-points with an expected miss criterion. Statist. Decisions, 21(1):3–13, 2003. [KS98] I. Karatzas and S. E. Shreve. Methods of Mathematical Finance, volume 39 of Applications of Mathematics. Springer-Verlag, New York, 1998. [LMW00] A. W. Lo, H. Mamaysky, and J. Wang. Foundations of technical analysis: Computational algorithms, statistical inference, and empirical implementation. Journal of Finance, LV(4):1705–1770, 2000.
K − 1 the successive updates (where T = Kh for some K ∈ N) √ (2) Xk+1 = Xk + µ(Xk )h + σ(Xk ) hξk+1 . d. standard normal with zero mean and unit variance. We denote such random variables as ξ ∼ N (0, 1). It is well known, that under some continuity and growth conditions on the coefficients σ(·) and µ(·), method (2) is then accurate of first order in the weak sense. t. |E[f (X(T ))] − E[f (XK )]| ≤ Cf h, h→0, (3) where F is a suitable class of test functions and the constant Cf depends on the function f but is independent of h.
Its hypograph (or lower graph) Hypo (φ) is defined by reversing the inequality. Further, given a sequence (φn )n≥1 of functions from E into R, the functions epi − lim infφn and epi − lim supφn are defined on E by epi−lim infφn (x) = sup lim inf inf φn (y) , (2) epi − lim supφn (x) = sup lim sup inf φn (y) , (3) k≥1 n→∞ y∈B(x,1/k) k≥1 n→∞ y∈B(x,1/k) where B (x, 1/k) denotes the open ball of radius 1/k centered at x. These functions are called respectively the lower epi-limit and the upper epi-limit of (φn )n≥1 .