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We apply\nour new method to the Ait-Sahalia model and propose an explicit\nand positivity preserving numerical scheme.<\/jats:p>","DOI":"10.1515\/mcma-2016-0113","type":"journal-article","created":{"date-parts":[[2016,10,9]],"date-time":"2016-10-09T10:01:28Z","timestamp":1476007288000},"page":"277-289","source":"Crossref","is-referenced-by-count":3,"title":["On the construction of boundary preserving numerical schemes"],"prefix":"10.1515","volume":"22","author":[{"given":"Nikolaos","family":"Halidias","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of the Aegean, Karlovassi 83200 Samos, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2016,10,9]]},"reference":[{"key":"2023040102000344059_j_mcma-2016-0113_ref_001_w2aab2b8d252b1b7b1ab2ab1Aa","doi-asserted-by":"crossref","unstructured":"Ait-Sahalia Y.,\nTesting continuous-time models of the spot interest rate,\nRev. Financ. Stud. 9 (1996), no. 2, 385\u2013426.","DOI":"10.1093\/rfs\/9.2.385"},{"key":"2023040102000344059_j_mcma-2016-0113_ref_002_w2aab2b8d252b1b7b1ab2ab2Aa","doi-asserted-by":"crossref","unstructured":"Dangerfield C. E., Kay D., MacNamara S. and Burrage K.,\nA boundary preserving numerical algorithm for the Wright\u2013Fisher model with mutation,\nBIT 52 (2012), no. 2, 283\u2013304.","DOI":"10.1007\/s10543-011-0351-3"},{"key":"2023040102000344059_j_mcma-2016-0113_ref_003_w2aab2b8d252b1b7b1ab2ab3Aa","doi-asserted-by":"crossref","unstructured":"Halidias N.,\nSemi-discrete approximations for stochastic differential equations and applications,\nInt. J. Comput. Math. 89 (2012), no. 6, 780\u2013794.","DOI":"10.1080\/00207160.2012.658380"},{"key":"2023040102000344059_j_mcma-2016-0113_ref_004_w2aab2b8d252b1b7b1ab2ab4Aa","doi-asserted-by":"crossref","unstructured":"Halidias N.,\nA novel approach to construct numerical methods for stochastic differential equations,\nNumer. Algorithms 66 (2014), no. 1, 79\u201387.","DOI":"10.1007\/s11075-013-9724-9"},{"key":"2023040102000344059_j_mcma-2016-0113_ref_005_w2aab2b8d252b1b7b1ab2ab5Aa","doi-asserted-by":"crossref","unstructured":"Halidias N.,\nA new numerical scheme for the CIR process,\nMonte Carlo Methods Appl. 21 (2015), no. 3, 245\u2013253.","DOI":"10.1515\/mcma-2015-0101"},{"key":"2023040102000344059_j_mcma-2016-0113_ref_006_w2aab2b8d252b1b7b1ab2ab6Aa","doi-asserted-by":"crossref","unstructured":"Halidias N.,\nAn explicit and positivity preserving numerical scheme for the mean reverting CEV model,\nJapan J. Indust. Appl. Math. 32 (2015), 545\u2013552.","DOI":"10.1007\/s13160-015-0183-7"},{"key":"2023040102000344059_j_mcma-2016-0113_ref_007_w2aab2b8d252b1b7b1ab2ab7Aa","doi-asserted-by":"crossref","unstructured":"Halidias N.,\nConstructing positivity preserving numerical schemes for the two-factor CIR model,\nMonte Carlo Methods Appl. 21 (2015), no. 4, 313\u2013323.","DOI":"10.1515\/mcma-2015-0109"},{"key":"2023040102000344059_j_mcma-2016-0113_ref_008_w2aab2b8d252b1b7b1ab2ab8Aa","doi-asserted-by":"crossref","unstructured":"Halidias N.,\nConstruction of positivity preserving numerical schemes for multidimensional stochastic differential equations,\nDiscrete Contin. Dyn. Syst. Ser. B 20 (2015), 153\u2013160.","DOI":"10.3934\/dcdsb.2015.20.153"},{"key":"2023040102000344059_j_mcma-2016-0113_ref_009_w2aab2b8d252b1b7b1ab2ab9Aa","doi-asserted-by":"crossref","unstructured":"Halidias N. and Stamatiou I.,\nApproximating explicitly the mean-reverting CEV process,\nJ. Probab. 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