{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:43:33Z","timestamp":1787330613840,"version":"build-2736575974"},"reference-count":17,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>We consider a wavelet Galerkin scheme for solving partial integrodifferential equations arising from option pricing in multidimensional L\u00e9vy models. Sparse tensor product spaces are applied for the discretization to reduce the complexity in the number of degrees of freedom, and wavelet compression methods are used to decrease the number of nonzero matrix entries. We focus on algorithmic details of the scheme, in particular on the numerical integration of the matrix coefficients.<\/jats:p>","DOI":"10.1137\/090760143","type":"journal-article","created":{"date-parts":[[2010,6,3]],"date-time":"2010-06-03T18:07:05Z","timestamp":1275588425000},"page":"1545-1566","source":"Crossref","is-referenced-by-count":3,"title":["Wavelet Galerkin Schemes for Multidimensional Anisotropic Integrodifferential Operators"],"prefix":"10.1137","volume":"32","author":[{"given":"C.","family":"Winter","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,6,3]]},"reference":[{"key":"R1","unstructured":"A. Chernov, T. von Petersdorff, and C. Schwab,\n                      Exponential Convergence of $hp$ Quadrature for Integral Operators with Gevrey Kernels\n                      , Research report 2009\u201303, Seminar for Applied Mathematics, ETH Z\u00fcrich, Z\u00fcrich, Switzerland, 2009."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142903428852"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/BF02072014"},{"key":"R4","unstructured":"P. J. Davis and P. Rabinowitz,\n                      Methods of Numerical Integration\n                      , Academic Press, New York, London, 1975."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202507002327"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827503429387"},{"key":"R7","unstructured":"Y. Meyer,\n                      Ondelettes et op\u00e9rateurs\n                      . II,\n                      Actualit\u00e9s Math\u00e9matiques\n                      , Hermann, Paris, 1990."},{"key":"R8","doi-asserted-by":"crossref","unstructured":"S. M. Nikol$'$ski\u0131\u02d8,\n                      Approximation of Functions of Several Variables and Imbedding Theorems\n                      , Grundlehren Math. Wiss. 205, Springer-Verlag, New York, 1975.","DOI":"10.1007\/978-3-642-65711-5"},{"key":"R9","doi-asserted-by":"crossref","unstructured":"N. Reich,\n                      Wavelet Compression of Anisotropic Integrodifferential Operators on Sparse Tensor Product Spaces\n                      , Ph.D. thesis, ETH Z\u00fcrich, Z\u00fcrich, Switzerland, 2008.","DOI":"10.1051\/m2an\/2009039"},{"key":"R10","unstructured":"N. Reich, C. Schwab, and C. Winter,\n                      On Kolmogorov Equations for Anisotropic Multivariate L\u00e9vy Processes\n                      , Research report 2008-03, Seminar for Applied Mathematics, ETH Z\u00fcrich, Z\u00fcrich, Switzerland, 2008."},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/0907058"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050311"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1007\/BF02252988"},{"key":"R14","doi-asserted-by":"crossref","unstructured":"T. von Petersdorff and C. Schwab,\n                      Fully discrete multiscale Galerkin BEM\n                      , in Multiscale Wavelet Methods for Partial Differential Equations, W. Dahmen, A. Kurdila, and P. Oswald, eds., Wavelet Anal. Appl. 6, Academic Press, San Diego, CA, 1997, pp. 287\u2013346.","DOI":"10.1016\/S1874-608X(97)80009-X"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1051\/m2an:2004005"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142994272957"},{"key":"R17","unstructured":"C. Winter,\n                      Wavelet Galerkin Schemes for Option Pricing in Multidimensional L\u00e9vy Models\n                      , Ph.D. thesis, ETH Z\u00fcrich, Z\u00fcrich, Switzerland, 2009."}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/090760143","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:16:06Z","timestamp":1787328966000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/090760143"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":17,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/090760143"],"URL":"https:\/\/doi.org\/10.1137\/090760143","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}