Asymptotic series for singularly perturbed Kolmogorov-Fokker-Planck equations

Journal Article · Sun Dec 01 04:00:00 EST 1996 · SIAM Journal of Applied Mathematics

DOI:https://doi.org/10.1137/S0036139994270085· OSTI ID:418060

Khasminskii, R Z; Yin, G ^[1]

---

1. Wayne State Univ., Detroit, MI (United States). Dept. of Mathematics

The authors derive limit theorems for the transition densities of diffusion processes and develop asymptotic expansions for solutions of a class of singularly perturbed Kolmogorov-Fokker-Planck equations. The model under consideration can be viewed as a Markov process having two time scales. One of them is a rapidly changing scale, and the other is a slowly varying one. The study is motivated by a wide range of applications involving singularly perturbed Markov processes in manufacturing systems, reliability analysis, queueing networks, statistical physics, population biology, financial economics, and many other related fields. In this work, the asymptotic expansion is constructed explicitly. It is shown that the initial layer terms in the expansion decay at an exponential rate. Error bounds on the remainder terms also are obtained. The validity of the expansion is rigorously justified.

• Sponsoring Organization: USDOE
• OSTI ID: 418060
• Journal Information: SIAM Journal of Applied Mathematics, Journal Name: SIAM Journal of Applied Mathematics Journal Issue: 6 Vol. 56; ISSN 0036-1399; ISSN SMJMAP
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ASYMPTOTIC SOLUTIONS
BROWNIAN MOVEMENT
CHAPMAN-KOLMOGOROV EQUATION
DIFFUSION
LIMITING VALUES
MARKOV PROCESS
MATHEMATICS
USES