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Schauder ベースによるブラウン運動表現の微妙な偏差を検出する
1MEMOTEF, Sapienza University of Rome, Roma 00161, Italy.
Chaos (Woodbury, N.Y.)
|September 4, 2025
まとめ
シャウダー表現を使って 代理ブラウン運動を生成しました 非ガウスのバージョンはいくつかの性質を模倣しますが,ブラウンの運動のランダム性とスペクトルの振る舞いを本当に複製するのはガウスの構造だけです.
科学分野:
- ストキャスティック・プロセス
- 数学金融
- タイムシリーズ分析
背景:
- ランダム現象のモデル化には ブラウン運動が不可欠です
- 真のブラウン運動と代替運動の区別は,正確な分析に不可欠です.
- シュオーダー表示は,ストキャスティックプロセスを構築するための方法を提供します.
研究 の 目的:
- 代用ストキャスティックプロセスを構築し分析する.
- ブラウンの運動と比較して,非ガウスの Schauder ベースの構造の忠誠性を調査する.
- 生成されたサンプル経路における真のブラウン運動からの微妙な偏差を識別する.
主な方法:
- ストキャスティックプロセスの構築に Schauder 表現を使用する.
- 非ガウス分布 (ベータ,均一) を用いてシャウダー係数.
- エントロピーベースの測定法とスペクトル分散分析を適用し,より深い評価を行う.
主要な成果:
- 非ガウス代用は二次変数や共変数構造のような性質を保ちました
- ガウス基構造のみが一貫したスペクトル行動とランダム性を維持した.
- ブラウン運動からの微妙な,しかし重要な偏差は,非ガウスの変数で観察されました.
結論:
- ショウダー表現は現実的なブラウン運動代理を生成できる.
- 真のブラウン運動特性を複製する上で優れている.
- ストキャスティックプロセスの微妙な差異を検出するには,高度な分析技術が必要です.
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