The transformation problem of Kolmogorov equations for one-dimensional diffusion processes to the Kolmogorov equation for the standard Wiener process analysed by I. D. Cherkasov [Teor. Veroyatn. Primen. 2, 384–388 (1957; Zbl. 81, 135)] and L. M. Ricciardi [J. Math. Anal. Appl. 54, 185–199 (1976; Zbl. 361.60043)] is reconsidered in the light of the contributions successively due to G. W. Bluman [SIAM J. Appl. Math. 39, 239–247 (1980; Zbl. 448.60056)] and I. D. Cherkasov [Sov. Math., Dokl. 21, 175–180 (1980; Zbl. 458.60075)]. In particular, the problem of boundary transformations is raised. Two examples are discussed in which the standard Wiener process is transformed first into itself and then into the Feller process.
On the transformation of diffusion equations and boundaries into the Kolmogorov equation for the Wiener process / L., Sacerdote; Ricciardi, LUIGI MARIA. - In: RICERCHE DI MATEMATICA. - ISSN 0035-5038. - STAMPA. - 41:1(1994), pp. 123-135.
On the transformation of diffusion equations and boundaries into the Kolmogorov equation for the Wiener process
RICCIARDI, LUIGI MARIA
1994
Abstract
The transformation problem of Kolmogorov equations for one-dimensional diffusion processes to the Kolmogorov equation for the standard Wiener process analysed by I. D. Cherkasov [Teor. Veroyatn. Primen. 2, 384–388 (1957; Zbl. 81, 135)] and L. M. Ricciardi [J. Math. Anal. Appl. 54, 185–199 (1976; Zbl. 361.60043)] is reconsidered in the light of the contributions successively due to G. W. Bluman [SIAM J. Appl. Math. 39, 239–247 (1980; Zbl. 448.60056)] and I. D. Cherkasov [Sov. Math., Dokl. 21, 175–180 (1980; Zbl. 458.60075)]. In particular, the problem of boundary transformations is raised. Two examples are discussed in which the standard Wiener process is transformed first into itself and then into the Feller process.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
