Beyond Galton-Watson Processes: Forests, Duals, and Ranks

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dc.contributor.authorJagers, Jonas
dc.contributor.departmentChalmers tekniska högskola / Institutionen för matematiska vetenskapersv
dc.contributor.departmentChalmers University of Technology / Department of Mathematical Sciencesen
dc.date.accessioned2019-07-03T14:38:24Z
dc.date.available2019-07-03T14:38:24Z
dc.date.issued2017
dc.description.abstractA random forest is a random graph (V,E) with a set of vertices V = N20 and a set of edges E = {ev, v 2 V } satisfying the following property: if v = (x, t + 1), then ev = (v, v0), where v0 = (x0, t) and x0 = 't(x) is an increasing stochastic process in x. For a given forest, there is a unique way to draw a dual forest. These forests can be used as a graphical representation of discrete time reproduction processes forward and backward in time. They also serve to introduce a new concept, ranked Galton-Watson processes, where individual reproduction depends on the position in the population. A main result is that the dual process to a Galton-Watson process in varying environments with immigration is a Galton-Watson process in varying environments if and only if the reproduction and immigration laws of the first process are linear fractional.
dc.identifier.urihttps://hdl.handle.net/20.500.12380/252196
dc.language.isoeng
dc.setspec.uppsokPhysicsChemistryMaths
dc.subjectMatematik
dc.subjectMathematics
dc.titleBeyond Galton-Watson Processes: Forests, Duals, and Ranks
dc.type.degreeExamensarbete för masterexamensv
dc.type.degreeMaster Thesisen
dc.type.uppsokH
local.programmeEngineering mathematics and computational science (MPENM), MSc
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