Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 59, Number 4 (2007), 971-983.
Conditional distributions which do not satisfy the Chapman-Kolmogorov equation
We consider one-dimensional generalized diffusion processes (ODGDPs for brief), where both boundary points are accessible or asymptotically accessible. For such ODGDPs we consider stochastic processes induced by conditioning on hitting or asymptotical hitting the right boundary point before hitting or asymptotical hitting the left boundary point. The induced stochastic processes are again ODGDPs when the right boundary point is either accessible with the absorbing boundary condition or asymptotically accessible. However the probability distributions of the induced stochastic processes do not satisfy the Chapman-Kolmogorov equation when the right boundary point is accessible with the reflecting or elastic boundary condition.
J. Math. Soc. Japan, Volume 59, Number 4 (2007), 971-983.
First available in Project Euclid: 10 December 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J60: Diffusion processes [See also 58J65]
Secondary: 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx] 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07]
IIZUKA, Masaru; MAENO, Miyuki; TOMISAKI, Matsuyo. Conditional distributions which do not satisfy the Chapman-Kolmogorov equation. J. Math. Soc. Japan 59 (2007), no. 4, 971--983. doi:10.2969/jmsj/05940971. https://projecteuclid.org/euclid.jmsj/1197320622