Holdings: Stochastic differential equations, backward SDEs, partial differential equations

Stochastic differential equations, backward SDEs, partial differential equations:

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Bibliographic Details
Main Authors:	Pardoux, Etienne 1947- (Author), Rascanu, Aurel (Author)
Format:	Electronic eBook
Language:	English
Published:	Cham [u.a.] Springer 2014
Series:	Stochastic modelling and applied probability 69
Subjects:	Stochastische Differentialgleichung
Online Access:	BTU01 FRO01 TUM01 UBA01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract
Physical Description:	1 Online-Ressource
ISBN:	9783319057132 9783319057149
DOI:	10.1007/978-3-319-05714-9

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Record in the Search Index

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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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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
url	https://doi.org/10.1007/978-3-319-05714-9 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 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
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