Stochastic Modeling and Simulation of Microscopic Processes
(2013) In Bachelor's Theses in Mathematical Sciences NUMK01 20132Mathematics (Faculty of Engineering)
 Abstract
 In this thesis we study analytical and numerical methods which describe interactions and evolution of complex physical systems modeled by microscopic processes. We focus on two types of systems which are differentiated based on how modeling is taking place at the microscopic level. In that respect we study systems which can be described either by stochastic differential equations or by elementary microscopic stochastic processes.
For the case of stochastic differential equations, we illustrate how to produce their solutions both analytically and numerically. For the case of elementary microscopic stochastic processes it is unrealistic to expect that an analytic solution would always exist since often such systems can be transient and out... (More)  In this thesis we study analytical and numerical methods which describe interactions and evolution of complex physical systems modeled by microscopic processes. We focus on two types of systems which are differentiated based on how modeling is taking place at the microscopic level. In that respect we study systems which can be described either by stochastic differential equations or by elementary microscopic stochastic processes.
For the case of stochastic differential equations, we illustrate how to produce their solutions both analytically and numerically. For the case of elementary microscopic stochastic processes it is unrealistic to expect that an analytic solution would always exist since often such systems can be transient and out of equilibrium. We therefore produce numerical solutions for those systems which are based on Monte Carlo simulations.
We constitute the respective analytic solutions and numerical methods from two vastly different research areas such as finance and traffic flow in order to better illustrate the wide applicability of such methods (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/studentpapers/record/4249084
 author
 Andersson, Andreas ^{LU}
 supervisor

 Alexandros Sopasakis ^{LU}
 organization
 course
 NUMK01 20132
 year
 2013
 type
 M2  Bachelor Degree
 subject
 publication/series
 Bachelor's Theses in Mathematical Sciences
 report number
 LUNFMA40022013
 ISSN
 16546229
 other publication id
 2013:K15
 language
 English
 id
 4249084
 date added to LUP
 20140214 16:28:17
 date last changed
 20151214 13:32:12
@misc{4249084, abstract = {In this thesis we study analytical and numerical methods which describe interactions and evolution of complex physical systems modeled by microscopic processes. We focus on two types of systems which are differentiated based on how modeling is taking place at the microscopic level. In that respect we study systems which can be described either by stochastic differential equations or by elementary microscopic stochastic processes. For the case of stochastic differential equations, we illustrate how to produce their solutions both analytically and numerically. For the case of elementary microscopic stochastic processes it is unrealistic to expect that an analytic solution would always exist since often such systems can be transient and out of equilibrium. We therefore produce numerical solutions for those systems which are based on Monte Carlo simulations. We constitute the respective analytic solutions and numerical methods from two vastly different research areas such as finance and traffic flow in order to better illustrate the wide applicability of such methods}, author = {Andersson, Andreas}, issn = {16546229}, language = {eng}, note = {Student Paper}, series = {Bachelor's Theses in Mathematical Sciences}, title = {Stochastic Modeling and Simulation of Microscopic Processes}, year = {2013}, }