Asymptotic expansions for SDE's with small multiplicative noise
Sergio Albeverio, Boubaker Smii
TL;DR
This paper develops asymptotic power series expansions for stochastic differential equations with small multiplicative noise, providing detailed estimates on the remainders to understand the behavior of solutions.
Contribution
It introduces a method to derive asymptotic expansions for SDEs with small multiplicative noise, including precise remainder estimates, advancing analytical tools in stochastic analysis.
Findings
Derived asymptotic expansions for SDEs with small multiplicative noise
Provided detailed estimates on the remainders of the expansions
Enhanced understanding of the solution behavior in small noise regimes
Abstract
Asymptotic expansions are derived as power series in a small coefficient entering a nonlinear multiplicative noise and a deterministic driving term in a nonlinear evolution equation. Detailed estimates on remainders are provided.
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Taxonomy
TopicsStochastic processes and financial applications · Advanced Mathematical Modeling in Engineering · Stochastic processes and statistical mechanics