This book presents the refereed proceedings of the 15th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held in Linz, Austria, and organized by the Johannes Kepler University Linz and the Austrian Academy of Sciences, in July 2022. These biennial conferences are major events for Monte Carlo and quasi-Monte Carlo researchers. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. Offering information on the latest developments in these highly active areas, this book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems, in particular arising in finance, statistics and computer graphics.
Part I Invited Articles: C. A. Beschle, A. Barth, Quasi Continuous Level Monte Carlo for Random Elliptic PDEs.- M. B. Giles, MLMC Techniques for Discontinuous Functions.- T. Helin, A. M. Stuart, A. L. Teckentrup, K. C. Zygalakis, Introduction to Gaussian Process Regression in Bayesian Inverse Problems, with new Results on Experimental Design for Weighted Error Measures.- V. Kaarnioja, Frances Y. Kuo, Ian H. Sloan, Lattice-Based Kernel Approximation and Serendipitous Weights for Parametric PDEs in Very High Dimensions.- E. Novak, Optimal Algorithms for Numerical Integration: Recent Results and Open Problems.- Chris. J. Oates, Minimum Kernel Discrepancy Estimators.- Gabriel Stoltz, Error Estimates and Variance Reduction for Nonequilibrium Stochastic Dynamics.- Part II Contributed Articles: F. Bernal, A. Berridi, Heuristics for the Probabilistic Solution of BVPs with Mixed Boundary Conditions.- Sou-Cheng T. Choi, Y. Ding, Fred J. Hickernell, J. Rathinavel, Aleksei G. Sorokin, Challenges in Developing Great Quasi-Monte Carlo Software.- L. Enzi, S. Thonhauser, Numerical Computation of Risk Functionals in PDMP Risk Models.- J. Fiedler, M. Gnewuch, Christian Weiß, New Bounds for the Extreme and the Star Discrepancy of Double-Infinite Matrices.- C. García-Pareja, F. Nobile, Unbiased Likelihood Estimation of Wright-Fisher Diffusion Processes.- Alexander D. Gilbert, Frances Y. Kuo, Ian H. Sloan, A. Srikumar, Theory and Construction of Quasi-Monte Carlo Rules for Asian Option Pricing and Density Estimation.- Philipp A. Guth, V. Kaarnioja, Application of Dimension Truncation Error Analysis to High Dimensional Function Approximation in Uncertainty Quantification.- Rami El Haddad, C. Lécot, Pierre L’Ecuyer, Simple Stratified Sampling for Simulating Multi-Dimensional Markov Chains.- K. Harsha, M. Gnewuch, M. Wnuk, Infinite-Variate 𝐿2-Approximation with Nested Subspace Sampling.- S. Heinrich, Randomized Complexity of Vector-Valued Approximation.-
A. Keller, C. Wächter, N. Binder, Quasi-Monte Carlo Algorithms (not only) for Graphics Software.- S. Krumscheid, Per Pettersson, Sequential Estimation using Hierarchically Stratified Domains with Latin Hypercube Sampling.- Frances Y. Kuo, Weiwen Mo, D. Nuyens, Ian H. Sloan, A. Srikumar, Comparison of Two Search Criteria for Lattice-based Kernel Approximation.- M. Longo, C. Schwab, A. Stein, A-posteriori QMC-FEM Error Estimation for Bayesian Inversion and Optimal Control with Entropic Risk Measure.- E. Løvbak, F. Blondeel, A. Lee, L. Vanroye, Andreas Van Barel, G. Samaey, Reversible Random Number Generation for Adjoint Monte Carlo Simulation of the Heat Equation.- H. Maatouk, D. Rullière, X. Bay, Large Scale Gaussian Processes with Matheron’s Update Rule and Karhunen-Loève Expansion.- A. Mickel, A. Neuenkirch, The Order Barrier for the 𝐿1-approximation of the Log-Heston SDE at a Single Point.- D. Nuyens, L. Wilkes, A Randomised Lattice Rule Algorithm with Pre-determined Generating Vector and Random Number of Points for Korobov Spaces with 0 < 𝛼 ≤ 1/2.- L. Paulin, D. Coeurjolly, N. Bonneel, Jean-Claude Iehl, V. Ostromoukhov, A. Keller, Generator Matrices by Solving Integer Linear Programs.- K. Ravi, T. Neckel, Hans-Joachim Bungartz, Multi-fidelity No-U-Turn Sampling.- C. Reisinger, M. Olympia Tsianni, Convergence of the Euler–Maruyama Particle Scheme for a Regularised McKean–Vlasov Equation Arising from the Calibration of Local-stochastic Volatility models.- A. G. Sorokin, J. Rathinavel, On Bounding and Approximating Functions of Multiple Expectations using Quasi-Monte Carlo.- K. Spendier, M. Szölgyenyi, Convergence of the Tamed-Euler–Maruyama Method for SDEs with Discontinuous and Polynomially Growing Drift.- Víctor de la Torre, J. Marzo, QMC Strength for some Random Configurations on the Sphere.- P. Vanmechelen, G. Lombaert, G. Samaey, Multilevel MCMC with Level-Dependent Data in a Model Case of Structural Damage Assessment.- M. Wnuk, A Note on Compact Embeddings of Reproducing Kernel Hilbert Spaces in 𝐿2 and Infinite-variate Function Approximation.
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