메뉴 건너뛰기




Volumn 102, Issue 3, 1999, Pages 555-591

Singularly perturbed switching diffusions: Rapid switchings and fast diffusions

Author keywords

Asymptotic expansion; Kolmogorov forward equation; Singular perturbation

Indexed keywords

ASYMPTOTIC ANALYSIS; MARKOV PROCESSES; PERTURBATION TECHNIQUES;

EID: 0033245911     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022698023010     Document Type: Article
Times cited : (19)

References (33)
  • 1
    • 0001673895 scopus 로고
    • Asymptotic behavior of solutions of parabolic equations and ergodic properties of nonhomogeneous diffusion processes
    • 1. IL'IN, A. M., and KHASMINSKII, R. Z., Asymptotic Behavior of Solutions of Parabolic Equations and Ergodic Properties of Nonhomogeneous Diffusion Processes, Matematicheskii Sbornik, Vol. 60, pp. 366-392, 1963.
    • (1963) Matematicheskii Sbornik , vol.60 , pp. 366-392
    • Il'in, A.M.1    Khasminskii, R.Z.2
  • 2
    • 0000182826 scopus 로고
    • On an averaging principle for Itô stochastic differential equations
    • 2. KHASMINSKII, R. Z., On an Averaging Principle for Itô Stochastic Differential Equations, Kybernetika, Vol. 4, pp. 260-279, 1968.
    • (1968) Kybernetika , vol.4 , pp. 260-279
    • Khasminskii, R.Z.1
  • 3
    • 0030417026 scopus 로고    scopus 로고
    • Asymptotic series for singularly perturbed Kolmogorov-Fokker-Planck equations
    • 3. KHASMINSKII, R. Z., and YIN, G., Asymptotic Series for Singularly Perturbed Kolmogorov-Fokker-Planck Equations, SIAM Journal on Applied Mathematics, Vol. 56, pp. 1766-1793, 1996.
    • (1996) SIAM Journal on Applied Mathematics , vol.56 , pp. 1766-1793
    • Khasminskii, R.Z.1    Yin, G.2
  • 4
    • 0030084736 scopus 로고    scopus 로고
    • Asymptotic expansions of singularly perturbed systems involving rapidly fluctuating Markov chains
    • 4. KHASMINSKII, R. Z., YIN, G., and ZHANG, Q., Asymptotic Expansions of Singularly Perturbed Systems Involving Rapidly Fluctuating Markov Chains, SIAM Journal on Applied Mathematics, Vol. 56, pp. 277-293, 1996.
    • (1996) SIAM Journal on Applied Mathematics , vol.56 , pp. 277-293
    • Khasminskii, R.Z.1    Yin, G.2    Zhang, Q.3
  • 5
    • 0000506591 scopus 로고
    • The exit problem for randomly perturbed dynamical systems
    • 5. MATKOWSKY, B. J., and SCHUSS, Z., The Exit Problem for Randomly Perturbed Dynamical Systems, SIAM Journal on Applied Mathematics, Vol. 33, pp. 365-382, 1977.
    • (1977) SIAM Journal on Applied Mathematics , vol.33 , pp. 365-382
    • Matkowsky, B.J.1    Schuss, Z.2
  • 6
    • 0009139496 scopus 로고
    • Introduction to the asymptotic analysis of stochastic equations
    • American Mathematical Society
    • 6. PAPANICOLAOUS, G. C., Introduction to the Asymptotic Analysis of Stochastic Equations, Lectures in Applied Mathematics, American Mathematical Society, Vol. 16, pp. 109-147, 1977.
    • (1977) Lectures in Applied Mathematics , vol.16 , pp. 109-147
    • Papanicolaous, G.C.1
  • 8
    • 0040063549 scopus 로고    scopus 로고
    • Bound market structure in the presence of marked point processes
    • 8. BJÖRK, T., KABANOV, YU., and RUNGGALDIER, W., Bound Market Structure in the Presence of Marked Point Processes, Mathematical Finance, Vol. 7, pp. 211-239, 1997.
    • (1997) Mathematical Finance , vol.7 , pp. 211-239
    • Björk, T.1    Kabanov, Yu.2    Runggaldier, W.3
  • 10
    • 0019623485 scopus 로고
    • A singular perturbation approach to modelling and control of Markov chains
    • 10. PHILLIPS, R. G., and KOKOTOVIC, P. V., A Singular Perturbation Approach to Modelling and Control of Markov Chains, IEEE Transactions on Automatic Control, Vol. 26, pp. 1087-1094, 1981.
    • (1981) IEEE Transactions on Automatic Control , vol.26 , pp. 1087-1094
    • Phillips, R.G.1    Kokotovic, P.V.2
  • 12
    • 0002809590 scopus 로고
    • Switching processes: Averaging principle, diffusion approximation, and applications
    • 12. ANISIMOV, V. V., Switching Processes: Averaging Principle, Diffusion Approximation, and Applications, Acta Applicatae Mathematicae, Vol. 40, pp. 95-141, 1995.
    • (1995) Acta Applicatae Mathematicae , vol.40 , pp. 95-141
    • Anisimov, V.V.1
  • 14
    • 0003537039 scopus 로고
    • Asymptotic methods of the theory of stochastic differential equations
    • American Mathematical Society, Providence, Rhode Island
    • 14. SKOROHOD, A. V., Asymptotic Methods of the Theory of Stochastic Differential Equations, Translations of Mathematical Monographs, American Mathematical Society, Providence, Rhode Island, Vol. 78, 1989.
    • (1989) Translations of Mathematical Monographs , vol.78
    • Skorohod, A.V.1
  • 17
    • 0003179709 scopus 로고
    • Theory of random evolutions with applications to partial differential equations
    • 17. GRIEGO, R. J., and HERSH, R., Theory of Random Evolutions with Applications to Partial Differential Equations, Transactions of the American Mathematical Society, Vol. 156, pp. 405-418, 1971.
    • (1971) Transactions of the American Mathematical Society , vol.156 , pp. 405-418
    • Griego, R.J.1    Hersh, R.2
  • 19
    • 0002546882 scopus 로고
    • A limit theorem for perturbed operator semigroups with applications to random evolutions
    • 19. KURTZ, T. G., A Limit Theorem for Perturbed Operator Semigroups with Applications to Random Evolutions, Journal of Functional Analysis, Vol. 12, pp. 55-67, 1973.
    • (1973) Journal of Functional Analysis , vol.12 , pp. 55-67
    • Kurtz, T.G.1
  • 24
    • 0003954462 scopus 로고
    • Wiley Classic Library Edition, John Wiley, New York, New York
    • 24. DOOB, J. L., Stochastic Processes, Wiley Classic Library Edition, John Wiley, New York, New York, 1990.
    • (1990) Stochastic Processes
    • Doob, J.L.1
  • 26
    • 84974393405 scopus 로고
    • Partial differential systems with a small parameter and diffusion process with a discrete component
    • Mathematics of Random Media, Edited by W. E. Kohler and B. S. White, American Mathematical Society, Providence, Rhode Island
    • 26. EIZENBERG, A., and FREIDLIN, M., Partial Differential Systems with a Small Parameter and Diffusion Process with a Discrete Component, Mathematics of Random Media, Edited by W. E. Kohler and B. S. White, Lectures in Applied Mathematics, American Mathematical Society, Providence, Rhode Island, Vol. 27, pp. 175-184, 1991.
    • (1991) Lectures in Applied Mathematics , vol.27 , pp. 175-184
    • Eizenberg, A.1    Freidlin, M.2
  • 27
    • 0003419993 scopus 로고
    • North-Holland, New York, New York
    • 27. EIDELMAN, S. D., Parabolic Systems, North-Holland, New York, New York, 1969.
    • (1969) Parabolic Systems
    • Eidelman, S.D.1
  • 29
    • 0003223550 scopus 로고
    • Linear and quasi-linear equations of parabolic type
    • American Mathematical Society, Providence, Rhode Island
    • 29. LADYZHENSKAIA, O. A., SOLONNIKOV, V. A., and URAL'TSEVA, N., Linear and Quasi-Linear Equations of Parabolic Type, Translation of Mathematical Monographs, American Mathematical Society, Providence, Rhode Island, Vol. 23, 1968.
    • (1968) Translation of Mathematical Monographs , vol.23
    • Ladyzhenskaia, O.A.1    Solonnikov, V.A.2    Ural'tseva, N.3
  • 32
    • 0003218827 scopus 로고
    • Matching of asymptotic expansions of solutions of boundary value problems
    • American Mathematical Society, Providence, Rhode Island
    • 32. IL'IN, A. M., Matching of Asymptotic Expansions of Solutions of Boundary Value Problems, Translation of Mathematical Monographs, American Mathematical Society, Providence, Rhode Island, Vol. 102, 1992.
    • (1992) Translation of Mathematical Monographs , vol.102
    • Il'in, A.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.