Osaka Journal of Mathematics

Extensions of diffusion processes on intervals and Feller's boundary conditions

Kouji Yano

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Abstract

For a minimal diffusion process on $(a,b)$, any possible extension of it to a standard process on $[a,b]$ is characterized by the characteristic measures of excursions away from the boundary points $a$ and $b$. The generator of the extension is proved to be characterized by Feller's boundary condition.

Article information

Source
Osaka J. Math., Volume 51, Number 2 (2014), 375-405.

Dates
First available in Project Euclid: 8 April 2014

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1396966254

Mathematical Reviews number (MathSciNet)
MR3192547

Zentralblatt MATH identifier
1311.60089

Subjects
Primary: 60J50: Boundary theory
Secondary: 60J25: Continuous-time Markov processes on general state spaces 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07] 47D07: Markov semigroups and applications to diffusion processes {For Markov processes, see 60Jxx}

Citation

Yano, Kouji. Extensions of diffusion processes on intervals and Feller's boundary conditions. Osaka J. Math. 51 (2014), no. 2, 375--405. https://projecteuclid.org/euclid.ojm/1396966254


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