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Convergence of integral functionals of one-dimensional diffusions


 
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1. Title Title of document Convergence of integral functionals of one-dimensional diffusions
 
2. Creator Author's name, affiliation, country Aleksandar Mijatovic; Imperial College; United Kingdom
 
2. Creator Author's name, affiliation, country Mikhail Urusov; Universität Duisburg-Essen; Germany
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Integral functional; one-dimensional diffusion; local time; Bessel process; Ray-Knight theorem; Williams theorem
 
3. Subject Subject classification 60H10; 60J60
 
4. Description Abstract In this paper we describe the pathwise behaviour of the integral functional $\int_0^t f(Y_u)\,du$ for any $t\in[0,\zeta]$, where $\zeta$ is (a possibly infinite) exit time of a one-dimensional diffusion process $Y$ from its state space, $f$ is a nonnegative Borel measurable function and the coefficients of the SDE solved by $Y$ are only required to satisfy weak local integrability conditions. Two proofs of the deterministic characterisation of the convergence of such functionals are given: the problem is reduced in two different ways to certain path properties of Brownian motion where either the Williams theorem and the theory of Bessel processes or the first Ray-Knight theorem can be applied to prove the characterisation. As a simple application of the main results we give a short proof of Feller's test for explosion.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) London Mathematical Society and Mathematisches Forschungsinstitut Oberwolfach
 
7. Date (YYYY-MM-DD) 2012-12-16
 
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/1825
 
10. Identifier Digital Object Identifier 10.1214/ECP.v17-1825
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 17
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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