### Abstract

In this paper we deal with stochastic initial value problems which have three different scales of variations represented by a small parameter. We obtain a limit theorem of KHASMINSKII type on an asymptotically unbounded interval in a framework based on separable Banach spaces and evolution operators. The expectations of random propagators are approximated by a backward propagator solving a final value problem as the small parameter vanishes. This result can be applied to diffusion effects caused by multiple wave scattering in random media.

Original language | English |
---|---|

Pages (from-to) | 473-474 |

Number of pages | 2 |

Journal | ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik |

Volume | 76 |

Issue number | SUPPL. 3 |

Publication status | Published - 1996 Dec 1 |

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### All Science Journal Classification (ASJC) codes

- Computational Mechanics
- Applied Mathematics

### Cite this

*ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik*,

*76*(SUPPL. 3), 473-474.

}

*ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik*, vol. 76, no. SUPPL. 3, pp. 473-474.

**A limit theorem for stochastic initial value problems with multiscales.** / Kim, J. H.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A limit theorem for stochastic initial value problems with multiscales

AU - Kim, J. H.

PY - 1996/12/1

Y1 - 1996/12/1

N2 - In this paper we deal with stochastic initial value problems which have three different scales of variations represented by a small parameter. We obtain a limit theorem of KHASMINSKII type on an asymptotically unbounded interval in a framework based on separable Banach spaces and evolution operators. The expectations of random propagators are approximated by a backward propagator solving a final value problem as the small parameter vanishes. This result can be applied to diffusion effects caused by multiple wave scattering in random media.

AB - In this paper we deal with stochastic initial value problems which have three different scales of variations represented by a small parameter. We obtain a limit theorem of KHASMINSKII type on an asymptotically unbounded interval in a framework based on separable Banach spaces and evolution operators. The expectations of random propagators are approximated by a backward propagator solving a final value problem as the small parameter vanishes. This result can be applied to diffusion effects caused by multiple wave scattering in random media.

UR - http://www.scopus.com/inward/record.url?scp=33748812511&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33748812511&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33748812511

VL - 76

SP - 473

EP - 474

JO - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

JF - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

SN - 0044-2267

IS - SUPPL. 3

ER -