Show simple item record

dc.contributor.authorLuoto, Antti
dc.date.accessioned2018-11-16T10:16:50Z
dc.date.available2018-11-16T10:16:50Z
dc.date.issued2018
dc.identifier.isbn978-951-39-7576-0fi
dc.identifier.isbn978-951-39-7576-0
dc.identifier.otheroai:jykdok.linneanet.fi:1907539
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/60216
dc.description.abstractThis thesis addresses questions related to approximation arising from the fields of stochastic analysis and partial differential equations. Theoretical results regarding convergence rates are obtained by using discretization schemes where the limiting process, the Brownian motion, is approximated by a simple discrete-time random walk. The rate of convergence is derived for a finite-difference approximation of the solution of a terminal value problem for the backward heat equation. This weak approximation result is proved for a terminal function which has bounded variation on compact sets. The sharpness of the according rate is achieved by applying some new results related to the first exit time behavior of Brownian bridges. In addition, convergence rates in the L2-norm are proved for Markovian forward-backward stochastic differential equations, where the underlying forward process is either Brownian motion or a more general Itô diffusion.fi
dc.format.extent1 verkkoaineisto (24 sivua, 112 sivua useina numerointijaksoina, 4 numeroimatonta sivua)
dc.language.isoeng
dc.publisherUniversity of Jyväskylä
dc.relation.ispartofseriesReport / University of Jyväskylä, Department of Mathematics and Statistics
dc.subject.otherBrownian motion
dc.subject.otherapproximation
dc.subject.otherrandom walks
dc.subject.otherstochastic differential equations
dc.subject.otherbackward heat equation
dc.titleApproximation of heat equation and backward SDEs using random walk : convergence rates
dc.identifier.urnURN:ISBN:978-951-39-7576-0
dc.contributor.yliopistoUniversity of Jyväskyläen
dc.contributor.yliopistoJyväskylän yliopistofi
dc.contributor.oppiaineMatematiikkafi
dc.relation.issn1457-8905
dc.relation.numberinseries169
dc.rights.accesslevelopenAccessfi
dc.subject.ysoapproksimointi
dc.subject.ysostokastiset prosessit
dc.subject.ysoosittaisdifferentiaaliyhtälöt


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record