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dc.contributor.advisorÜnal, Gazanfer
dc.contributor.authorTerzi, Feleknaz Dilek
dc.date.accessioned2020-12-29T06:47:32Z
dc.date.available2020-12-29T06:47:32Z
dc.date.submitted2009
dc.date.issued2018-08-06
dc.identifier.urihttps://acikbilim.yok.gov.tr/handle/20.500.12812/339121
dc.description.abstractTek boyutlu Feynman-Kac teoreminin çok boyuta genişletilmesini kapsayan bu tez, özellikle stokastik diferansiyel denklemlerin sıçramalı ( jump ) difüzyon türü üzerinde durarak, çok önemli bir amaca hizmet etmiştir. Nitekim bu teorem aracılığıyla tek boyutlu belli sınır koşulları altında verilen bir kısmi integro-diferansiyel denklemin çözümünü kolayca elde edebiliyoruz. Bunun için, yeni analiz olarak adlandırılan stokastik analiz derslerine ihtiyacımız olduğundan, teoremi anlamak için gerekli olan tüm bilgiler uygulamalarıyla birlikte ekte bulunmaktadr.Sigortalamada olduğu kadar fizik, biyoloji, kimya, mikroelektronik, iktisat, yöneylem araştırmaları, finans ve çeşitli mühendislik uygulamaları gibi pek çok farklı alanda uygulama alanı bulan stokastik süreçlerle modelleme, son yıllarda yeryüzündeki geniş bir kitlenin ilgi alanı haline gelmiştir. 
dc.description.abstractIn this thesis, I will consider to extend the generalized Feynman-Kac Theorem for one-dimensional linear and jump diffusion stochastic differential equations to the generalized Feynman-Kac Theorem for n-dimensional linear and jump diffusion stochastic differential equations.Thanks to this theorem, we can easily obtain the solution of One Dimensional Partial Integro-Differential equation with boundary conditions which is given as propositions in this work. For an introduction of stochastic differential equations, I introduce the stochastic analysis which is known as a new calculus to the readers in Appendix.In recent years there has been a great interest in this subject, through models with stochastic processes, e.g. Brownian (diffusion) motion with drift, Poisson (jump) processes with drift, which are important for modeling insurance, as well as many other areas: physics, biology, chemistry, microelectronics, economics, operations research, finance and various engineering applications. In this work, basic probability definitions are presented briefly, then continuous-time diffusion processes, discontinuous jump processes and stochastic differential equations are explained in Appendix. Finally, two physical problems are solved as applications. en_US
dc.languageEnglish
dc.language.isoen
dc.rightsinfo:eu-repo/semantics/embargoedAccess
dc.rightsAttribution 4.0 United Statestr_TR
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectMatematiktr_TR
dc.subjectMathematicsen_US
dc.titleFeynman-kac theorem and its applications
dc.title.alternativeFeynman-kac teoremi ve uygulamaları
dc.typemasterThesis
dc.date.updated2018-08-06
dc.contributor.departmentMatematik Anabilim Dalı
dc.identifier.yokid10131527
dc.publisher.instituteFen Bilimleri Enstitüsü
dc.publisher.universityYEDİTEPE ÜNİVERSİTESİ
dc.identifier.thesisid452651
dc.description.pages72
dc.publisher.disciplineMatematiksel Fizik Bilim Dalı


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