### Abstract

Language | English |
---|---|

Pages | 141-167 |

Number of pages | 27 |

Journal | Proceedings of the Royal Society of Edinburgh, Section A: Mathematics |

Volume | 146 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2016 |

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**Short-time asymptotic expansions of semilinear evolution equations.** / Fahrenwaldt, Matthias Albrecht.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Short-time asymptotic expansions of semilinear evolution equations

AU - Fahrenwaldt, Matthias Albrecht

PY - 2016/1

Y1 - 2016/1

N2 - We develop an algebraic approach to constructing short-time asymptotic expansions of solutions of a class of abstract semilinear evolution equations. The expansions are typically valid for both the solution of the equation and its gradient. We apply a perturbation approach based on the symbolic calculus of pseudo-differential operators and heat kernel methods. The construction is explicit and can be done to arbitrary order. All results are rigorously formulated in terms of Banach algebras. As an application we obtain a novel approach to finding approximate solutions of Markovian backward stochastic differential equations.

AB - We develop an algebraic approach to constructing short-time asymptotic expansions of solutions of a class of abstract semilinear evolution equations. The expansions are typically valid for both the solution of the equation and its gradient. We apply a perturbation approach based on the symbolic calculus of pseudo-differential operators and heat kernel methods. The construction is explicit and can be done to arbitrary order. All results are rigorously formulated in terms of Banach algebras. As an application we obtain a novel approach to finding approximate solutions of Markovian backward stochastic differential equations.

U2 - 10.1017/S0308210515000372

DO - 10.1017/S0308210515000372

M3 - Article

VL - 146

SP - 141

EP - 167

JO - Proceedings of the Royal Society of Edinburgh, Section A: Mathematics

T2 - Proceedings of the Royal Society of Edinburgh, Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh, Section A: Mathematics

SN - 0308-2105

IS - 1

ER -