Stochastic Integration in Banach Spaces
Considering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena. By using such equations the present book introduces a new method for modeling the states of complex systems perturbed b...
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Springer
2015
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oai:scholar.dlu.edu.vn:DLU123456789-578472023-11-11T05:56:10Z Stochastic Integration in Banach Spaces Mandrekar, Vidyadhar Rüdiger, Barbara Banach spaces Stochastic processes Mathematics Considering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena. By using such equations the present book introduces a new method for modeling the states of complex systems perturbed by random sources over time, such as interest rates in financial markets or temperature distributions in a specific region. It studies properties of the solutions of the stochastic equations, observing the long-term behavior and the sensitivity of the solutions to changes in the initial data. The authors consider an integration theory of measurable and adapted processes in appropriate Banach spaces as well as the non-Gaussian case, whereas most of the literature only focuses on predictable settings in Hilbert spaces. The book is intended for graduate students and researchers in stochastic (partial) differential equations, mathematical finance and non-linear filtering and assumes a knowledge of the required integration theory, existence and uniqueness results and stability theory. The results will be of particular interest to natural scientists and the finance community. Readers should ideally be familiar with stochastic processes and probability theory in general, as well as functional analysis and in particular the theory of operator semigroups. 2015-08-31T03:36:20Z 2015-08-31T03:36:20Z 2015 Book 978-3-319-12853-5 https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/57847 en application/pdf Springer |
| institution |
Thư viện Trường Đại học Đà Lạt |
| collection |
Thư viện số |
| language |
English |
| topic |
Banach spaces Stochastic processes Mathematics |
| spellingShingle |
Banach spaces Stochastic processes Mathematics Mandrekar, Vidyadhar Rüdiger, Barbara Stochastic Integration in Banach Spaces |
| description |
Considering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena. By using such equations the present book introduces a new method for modeling the states of complex systems perturbed by random sources over time, such as interest rates in financial markets or temperature distributions in a specific region. It studies properties of the solutions of the stochastic equations, observing the long-term behavior and the sensitivity of the solutions to changes in the initial data. The authors consider an integration theory of measurable and adapted processes in appropriate Banach spaces as well as the non-Gaussian case, whereas most of the literature only focuses on predictable settings in Hilbert spaces. The book is intended for graduate students and researchers in stochastic (partial) differential equations, mathematical finance and non-linear filtering and assumes a knowledge of the required integration theory, existence and uniqueness results and stability theory. The results will be of particular interest to natural scientists and the finance community. Readers should ideally be familiar with stochastic processes and probability theory in general, as well as functional analysis and in particular the theory of operator semigroups. |
| format |
Book |
| author |
Mandrekar, Vidyadhar Rüdiger, Barbara |
| author_facet |
Mandrekar, Vidyadhar Rüdiger, Barbara |
| author_sort |
Mandrekar, Vidyadhar |
| title |
Stochastic Integration in Banach Spaces |
| title_short |
Stochastic Integration in Banach Spaces |
| title_full |
Stochastic Integration in Banach Spaces |
| title_fullStr |
Stochastic Integration in Banach Spaces |
| title_full_unstemmed |
Stochastic Integration in Banach Spaces |
| title_sort |
stochastic integration in banach spaces |
| publisher |
Springer |
| publishDate |
2015 |
| url |
https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/57847 |
| _version_ |
1819764973145948160 |