Individual Path Uniqueness of Solutions of Stochastic Differential Equations

Alexander M. Davie ()
Additional contact information
Alexander M. Davie: University of Edinburgh, School of Mathematics

A chapter in Stochastic Analysis 2010, 2011, pp 213-225 from Springer

Abstract: Abstract We consider the stochastic differential equation dx(t) = f(t, x(t))dt + b(t, x(t))dW(t), x(0) = x 0 for t ≥ 0, where x(t) ∈ ℝ d , W is a standard d-dimensional Brownian motion, f is a bounded Borel function from [0, ∞) ×ℝ d to ℝ d , and b is an invertible matrix-valued function satisfying some regularity conditions. We show that, for almost all Brownian paths W(t), there is a unique x(t) satisfying this equation, interpreted in a “rough path” sense.

Keywords: Stochastic Differential Equation; Strong Solution; Transition Density; Borel Function; Rough Path (search for similar items in EconPapers)
Date: 2011
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-15358-7_10

Ordering information: This item can be ordered from
http://www.springer.com/9783642153587

DOI: 10.1007/978-3-642-15358-7_10

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().