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Weak and strong solutions of general stochastic models

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1.	Title	Title of document	Weak and strong solutions of general stochastic models
2.	Creator	Author's name, affiliation, country	Thomas G. Kurtz; University of Wisconsin, Madison; United States
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	weak solution; strong solution; stochastic models; pointwise uniqueness; pathwise uniqueness; compatible solutions; stochastic differential equations; stochastic partial differential equations; backward stochastic differential equations; Meyer-Zheng condi
3.	Subject	Subject classification	60G05
4.	Description	Abstract	Typically, a stochastic model relates stochastic “inputs” and, perhaps, controls tostochastic “outputs”. A general version of the Yamada-Watanabe and Engelbert the-orems relating existence and uniqueness of weak and strong solutions of stochasticequations is given in this context. A notion of compatibility between inputs and out-puts is critical in relating the general result to its classical forebears. The usualformulation of stochastic differential equations driven by semimartingales does notrequire compatibility, so a notion of partial compatibility is introduced which doeshold. Since compatibility implies partial compatibility, classical strong uniquenessresults imply strong uniqueness for compatible solutions. Weak existence argumentstypically give existence of compatible solutions (not just partially compatible solu-tions), and as in the original Yamada-Watanabe theorem, existence of strong solutionsfollows.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	National Science Foundation grant DMS 11-06424
7.	Date	(YYYY-MM-DD)	2014-08-25
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/2833
10.	Identifier	Digital Object Identifier	10.1214/ECP.v19-2833
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 19
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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