On transition densities of singularly perturbed diffusions with fast and slow components

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

DOI:https://doi.org/10.1137/S0036139995282906· OSTI ID:418061

Khasminskii, R Z; Yin, G ^[1]

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

The authors derive asymptotic properties of transition densities for singularly perturbed diffusion processes with fast and slow components. The study focuses on the Kolmogorov-Fokker-Planck equations. The model can be viewed as a diffusion process having two time scales and is motivated by a wide variety of applications involving singularly perturbed Markov processes in manufacturing systems, homogenization, reliability analysis, queueing networks, statistical physics, population biology, financial economics, and many other related fields. By virtue of the methods of matched singular perturbation, asymptotic expansion is constructed for the transition density. The expansion includes both regular part and boundary layer corrections. Detailed justification of the asymptotic expansion is given, and error bounds are also provided.

• Sponsoring Organization: Office of Naval Research, Washington, DC (United States); National Science Foundation, Washington, DC (United States)
• OSTI ID: 418061
• Journal Information: SIAM Journal of Applied Mathematics, Journal Name: SIAM Journal of Applied Mathematics Journal Issue: 6 Vol. 56; ISSN SMJMAP; ISSN 0036-1399
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ASYMPTOTIC SOLUTIONS
BROWNIAN MOVEMENT
CHAPMAN-KOLMOGOROV EQUATION
DIFFUSION
MATHEMATICS
USES