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In this paper we establish the pathwise convergence of solutions to hybrid SDEs using space-grid discretizations. Though time-grid discretizations are a classical approach for simulation purposes, our space-grid discretization provides a link with multi-regime Markov-modulated Brownian motions. This connection allows us to explore aspects that have been largely unexplored in the hybrid SDE literature. Specifically, we exploit our convergence result to obtain efficient and computationally tractable approximations for first-passage probabilities and expected occupation times of the solutions to hybrid SDEs. Lastly, we illustrate the effectiveness of the resulting approximations through numerical examples.<\/jats:p>","DOI":"10.1017\/jpr.2025.10050","type":"journal-article","created":{"date-parts":[[2025,12,19]],"date-time":"2025-12-19T08:34:07Z","timestamp":1766133247000},"page":"623-647","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":2,"title":["Space-grid approximations of hybrid stochastic differential equations and first-passage properties"],"prefix":"10.1017","volume":"63","author":[{"given":"Hansjoerg","family":"Albrecher","sequence":"first","affiliation":[{"name":"University of Lausanne"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1710-7747","authenticated-orcid":false,"given":"Oscar","family":"Peralta","sequence":"additional","affiliation":[{"name":"Cornell University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2025,12,19]]},"reference":[{"key":"S0021900225100508_ref29","doi-asserted-by":"publisher","DOI":"10.1137\/16M1059357"},{"key":"S0021900225100508_ref31","doi-asserted-by":"publisher","DOI":"10.1017\/jpr.2021.30"},{"key":"S0021900225100508_ref22","volume-title":"Stochastic Differential Equations and Diffusion Processes","author":"Ikeda","year":"2014"},{"key":"S0021900225100508_ref37","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-015-2105-0"},{"key":"S0021900225100508_ref4","volume-title":"Applied Probability and Queues","author":"Asmussen","year":"2003"},{"key":"S0021900225100508_ref7","doi-asserted-by":"publisher","DOI":"10.1080\/03461230410000565"},{"key":"S0021900225100508_ref30","unstructured":"[30] Nguyen, G. 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