Stochastic differential equations, backward SDEs, partial differential equations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cham [u.a.]
Springer
2014
|
| Schriftenreihe: | Stochastic modelling and applied probability
69 |
| Schlagworte: | |
| Online-Zugang: | BTU01 FRO01 TUM01 UBA01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 9783319057132 9783319057149 |
| DOI: | 10.1007/978-3-319-05714-9 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804152403402948612 |
|---|---|
| adam_text | STOCHASTIC DIFFERENTIAL EQUATIONS, BACKWARD SDES, PARTIAL DIFFERENTIAL
EQUATIONS
/ PARDOUX, ETIENNE
: 2014
TABLE OF CONTENTS / INHALTSVERZEICHNIS
INTRODUCTION
BACKGROUND OF STOCHASTIC ANALYSIS
ITO’S STOCHASTIC CALCULUS
STOCHASTIC DIFFERENTIAL EQUATIONS
SDE WITH MULTIVALUED DRIFT
BACKWARD SDE
ANNEXES
BIBLIOGRAPHY
INDEX
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
STOCHASTIC DIFFERENTIAL EQUATIONS, BACKWARD SDES, PARTIAL DIFFERENTIAL
EQUATIONS
/ PARDOUX, ETIENNE
: 2014
ABSTRACT / INHALTSTEXT
THIS RESEARCH MONOGRAPH PRESENTS RESULTS TO RESEARCHERS IN STOCHASTIC
CALCULUS, FORWARD AND BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS,
CONNECTIONS BETWEEN DIFFUSION PROCESSES AND SECOND ORDER PARTIAL
DIFFERENTIAL EQUATIONS (PDES), AND FINANCIAL MATHEMATICS. IT PAYS
SPECIAL ATTENTION TO THE RELATIONS BETWEEN SDES/BSDES AND SECOND ORDER
PDES UNDER MINIMAL REGULARITY ASSUMPTIONS, AND ALSO EXTENDS THOSE
RESULTS TO EQUATIONS WITH MULTIVALUED COEFFICIENTS. THE AUTHORS PRESENT
IN PARTICULAR THE THEORY OF REFLECTED SDES IN THE ABOVE MENTIONED
FRAMEWORK AND INCLUDE EXERCISES AT THE END OF EACH CHAPTER. STOCHASTIC
CALCULUS AND STOCHASTIC DIFFERENTIAL EQUATIONS (SDES) WERE FIRST
INTRODUCED BY K. ITO IN THE 1940S, IN ORDER TO CONSTRUCT THE PATH OF
DIFFUSION PROCESSES (WHICH ARE CONTINUOUS TIME MARKOV PROCESSES WITH
CONTINUOUS TRAJECTORIES TAKING THEIR VALUES IN A FINITE DIMENSIONAL
VECTOR SPACE OR MANIFOLD), WHICH HAD BEEN STUDIED FROM A MORE ANALYTIC
POINT OF VIEW BY KOLMOGOROV IN THE 1930S. SINCE THEN, THIS TOPIC HAS
BECOME AN IMPORTANT SUBJECT OF MATHEMATICS AND APPLIED MATHEMATICS,
BECAUSE OF ITS MATHEMATICAL RICHNESS AND ITS IMPORTANCE FOR APPLICATIONS
IN MANY AREAS OF PHYSICS, BIOLOGY, ECONOMICS AND FINANCE, WHERE RANDOM
PROCESSES PLAY AN INCREASINGLY IMPORTANT ROLE. ONE IMPORTANT ASPECT IS
THE CONNECTION BETWEEN DIFFUSION PROCESSES AND LINEAR PARTIAL
DIFFERENTIAL EQUATIONS OF SECOND ORDER, WHICH IS IN PARTICULAR THE BASIS
FOR MONTE CARLO NUMERICAL METHODS FOR LINEAR PDES. SINCE THE PIONEERING
WORK OF PENG AND PARDOUX IN THE EARLY 1990S, A NEW TYPE OF SDES CALLED
BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS (BSDES) HAS EMERGED. THE TWO
MAIN REASONS WHY THIS NEW CLASS OF EQUATIONS IS IMPORTANT ARE THE
CONNECTION BETWEEN BSDES AND SEMILINEAR PDES, AND THE FACT THAT BSDES
CONSTITUTE A NATURAL GENERALIZATION OF THE FAMOUS BLACK AND SCHOLES
MODEL FROM MATHEMATICAL FINANCE, AND THUS OFFER A NATURAL MATHEMATICAL
FRAMEWORK FOR THE FORMULATION OF MANY NEW MODELS IN FINANCE
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
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| discipline | Mathematik |
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| spelling | Pardoux, Etienne 1947- Verfasser (DE-588)111361117 aut Stochastic differential equations, backward SDEs, partial differential equations Etienne Pardoux ; Aurel Răşcanu Cham [u.a.] Springer 2014 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Stochastic modelling and applied probability 69 Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 s 1\p DE-604 Rascanu, Aurel Verfasser aut Stochastic modelling and applied probability 69 (DE-604)BV035421331 69 https://doi.org/10.1007/978-3-319-05714-9 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027437067&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027437067&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Pardoux, Etienne 1947- Rascanu, Aurel Stochastic differential equations, backward SDEs, partial differential equations Stochastic modelling and applied probability Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| subject_GND | (DE-588)4057621-8 |
| title | Stochastic differential equations, backward SDEs, partial differential equations |
| title_auth | Stochastic differential equations, backward SDEs, partial differential equations |
| title_exact_search | Stochastic differential equations, backward SDEs, partial differential equations |
| title_full | Stochastic differential equations, backward SDEs, partial differential equations Etienne Pardoux ; Aurel Răşcanu |
| title_fullStr | Stochastic differential equations, backward SDEs, partial differential equations Etienne Pardoux ; Aurel Răşcanu |
| title_full_unstemmed | Stochastic differential equations, backward SDEs, partial differential equations Etienne Pardoux ; Aurel Răşcanu |
| title_short | Stochastic differential equations, backward SDEs, partial differential equations |
| title_sort | stochastic differential equations backward sdes partial differential equations |
| topic | Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| topic_facet | Stochastische Differentialgleichung |
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