Wishart processes

Wishart processes. Bru, M. Journal of Theoretical Probability, 4(4):725–751, October, 1991.

We propose some matrix generalizations of square Bessel processes and we indicate their first properties: hitting time of 0 of the smallest eigenvalue, additivity property, associated Martingales, distributions, which mainly extend the real-valued classical results. We explain why these processes are indecomposable and therefore differ from the real-valued ones. We conclude with some formulae concerning matrix quadratic functionals analogous to the Cameron Martin formula.

@article{bru_wishart_1991,
	title = {Wishart processes},
	volume = {4},
	issn = {1572-9230},
	url = {https://doi.org/10.1007/BF01259552},
	doi = {10.1007/BF01259552},
	abstract = {We propose some matrix generalizations of square Bessel processes and we indicate their first properties: hitting time of 0 of the smallest eigenvalue, additivity property, associated Martingales, distributions, which mainly extend the real-valued classical results. We explain why these processes are indecomposable and therefore differ from the real-valued ones. We conclude with some formulae concerning matrix quadratic functionals analogous to the Cameron Martin formula.},
	language = {en},
	number = {4},
	urldate = {2024-09-17},
	journal = {Journal of Theoretical Probability},
	author = {Bru, Marie-France},
	month = oct,
	year = {1991},
	keywords = {Bessel process, Cameron Martin formulae, Wishart distribution, matrix diffusions, special matrix functions},
	pages = {725--751},
}

Downloads: 0

{"_id":"PxnASG2i9dwgy6R2C","bibbaseid":"bru-wishartprocesses-1991","authorIDs":[],"author_short":["Bru, M."],"bibdata":{"bibtype":"article","type":"article","title":"Wishart processes","volume":"4","issn":"1572-9230","url":"https://doi.org/10.1007/BF01259552","doi":"10.1007/BF01259552","abstract":"We propose some matrix generalizations of square Bessel processes and we indicate their first properties: hitting time of 0 of the smallest eigenvalue, additivity property, associated Martingales, distributions, which mainly extend the real-valued classical results. We explain why these processes are indecomposable and therefore differ from the real-valued ones. We conclude with some formulae concerning matrix quadratic functionals analogous to the Cameron Martin formula.","language":"en","number":"4","urldate":"2024-09-17","journal":"Journal of Theoretical Probability","author":[{"propositions":[],"lastnames":["Bru"],"firstnames":["Marie-France"],"suffixes":[]}],"month":"October","year":"1991","keywords":"Bessel process, Cameron Martin formulae, Wishart distribution, matrix diffusions, special matrix functions","pages":"725–751","bibtex":"@article{bru_wishart_1991,\n\ttitle = {Wishart processes},\n\tvolume = {4},\n\tissn = {1572-9230},\n\turl = {https://doi.org/10.1007/BF01259552},\n\tdoi = {10.1007/BF01259552},\n\tabstract = {We propose some matrix generalizations of square Bessel processes and we indicate their first properties: hitting time of 0 of the smallest eigenvalue, additivity property, associated Martingales, distributions, which mainly extend the real-valued classical results. We explain why these processes are indecomposable and therefore differ from the real-valued ones. We conclude with some formulae concerning matrix quadratic functionals analogous to the Cameron Martin formula.},\n\tlanguage = {en},\n\tnumber = {4},\n\turldate = {2024-09-17},\n\tjournal = {Journal of Theoretical Probability},\n\tauthor = {Bru, Marie-France},\n\tmonth = oct,\n\tyear = {1991},\n\tkeywords = {Bessel process, Cameron Martin formulae, Wishart distribution, matrix diffusions, special matrix functions},\n\tpages = {725--751},\n}\n\n\n\n\n\n\n\n","author_short":["Bru, M."],"key":"bru_wishart_1991","id":"bru_wishart_1991","bibbaseid":"bru-wishartprocesses-1991","role":"author","urls":{"Paper":"https://doi.org/10.1007/BF01259552"},"keyword":["Bessel process","Cameron Martin formulae","Wishart distribution","matrix diffusions","special matrix functions"],"metadata":{"authorlinks":{}},"downloads":0,"html":""},"bibtype":"article","biburl":"https://bibbase.org/zotero/chiraaggohel","creationDate":"2020-01-31T19:54:15.079Z","downloads":0,"keywords":["bessel process","cameron martin formulae","wishart distribution","matrix diffusions","special matrix functions"],"search_terms":["wishart","processes","bru"],"title":"Wishart processes","year":1991,"dataSources":["nrXzNrxsNEnPJbYnT","akApyGuSiBYkDccny"]}