Dilation of Markovian cocycles on a von Neumann algebra
| dc.contributor.author | Goswami, Debashish | en |
| dc.contributor.author | Lindsay, J. M. | en |
| dc.contributor.author | Sinha, Kalyan B. | en |
| dc.contributor.author | Wills, Stephen J. | en |
| dc.date.accessioned | 2023-07-18T15:49:42Z | |
| dc.date.available | 2023-07-18T15:49:42Z | |
| dc.date.issued | 2003-10-01 | en |
| dc.description.abstract | We consider normal Markovian cocycles on a von Neumann algebra which are adapted to a Fock filtration. Every such cocycle k which is Markov-regular and consists of completely positive contractions is realised as a conditioned ∗-homomorphic cocycle. This amounts to a stochastic generalisation of a recent dilation result for norm-continuous normal completely positive contraction semigroups. To achieve this stochastic dilation we use the fact that k is governed by a quantum stochastic differential equation whose coefficient matrix has a specific structure, and extend a technique for obtaining stochastic flow generators from Markov semigroup generators, to the context of cocycles. Number/exchange-free dilatability is seen to be related to locality in the case where the cocycle is a Markovian semigroup. In the same spirit unitary dilations of Markov-regular contraction cocycles on a Hilbert space are also described. The paper ends with a discussion of connections with measure-valued diffusion. | en |
| dc.description.status | Peer reviewed | en |
| dc.description.version | Published Version | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.citation | Goswami, D., Lindsay, J.M., Sinha, K.B. and Wills, S.J. (2003) ‘Dilation of Markovian cocycles on a von Neumann algebra’, Pacific Journal of Mathematics, 211(2), pp. 221–247. https://doi.org/10.2140/pjm.2003.211.221 | en |
| dc.identifier.doi | 10.2140/pjm.2003.211.221 | en |
| dc.identifier.endpage | 247 | en |
| dc.identifier.issn | 0030-8730 | en |
| dc.identifier.issued | 2 | en |
| dc.identifier.journaltitle | Pacific Journal of Mathematics | en |
| dc.identifier.startpage | 221 | en |
| dc.identifier.uri | https://hdl.handle.net/10468/14750 | |
| dc.identifier.volume | 211 | en |
| dc.language.iso | en | en |
| dc.publisher | Mathematical Sciences Publishers (MSP) | en |
| dc.relation.ispartof | Pacific Journal of Mathematics | en |
| dc.rights | © 2003 Pacific Journal of Mathematics. | en |
| dc.subject | Markovian cocycles | en |
| dc.subject | Fock filtration | en |
| dc.subject | Von Neumann algebra | en |
| dc.title | Dilation of Markovian cocycles on a von Neumann algebra | en |
| dc.type | Article (peer-reviewed) | en |
| oaire.citation.issue | 2 | en |
| oaire.citation.volume | 211 | en |
