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Stochastic Modeling and Simulation of Microscopic Processes

Andersson, Andreas LU (2013) In Bachelor's Theses in Mathematical Sciences NUMK01 20132
Mathematics (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:
author
Andersson, Andreas LU
supervisor
organization
course
NUMK01 20132
year
type
M2 - Bachelor Degree
subject
publication/series
Bachelor's Theses in Mathematical Sciences
report number
LUNFMA-4002-2013
ISSN
1654-6229
other publication id
2013:K15
language
English
id
4249084
date added to LUP
2014-02-14 16:28:17
date last changed
2015-12-14 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         = {1654-6229},
  language     = {eng},
  note         = {Student Paper},
  series       = {Bachelor's Theses in Mathematical Sciences},
  title        = {Stochastic Modeling and Simulation of Microscopic Processes},
  year         = {2013},
}