This article analyzes the behavior of a Brownian fluctuation process under a mixed strategic game setup. A variant of a compound Brownian motion has been newly proposed, which is called the Shifted Brownian Fluctuation Process to predict the turning points of a stochastic process. This compound process evolves until it reaches one step prior to the turning point. The Shifted Brownian Fluctuation Game has been constructed based on this new process to find the optimal moment of actions. Analytically tractable results are obtained by using the fluctuation theory and the mixed strategy game theory. The joint functional of the Shifted Brownian Fluctuation Process is targeted for transformation of the first passage time and its index. These results enable us to predict the moment of a turning point and the moment of actions to obtain the optimal payoffs of a game. This research adapts the theoretical framework to implement an autonomous trader for value assets including stocks and cybercurrencies.
翻译：文章分析了在混合战略游戏设置下布朗州波动过程的行为。 一个新提出了布朗州复合运动的变体, 称为布朗州变体变化过程, 以预测随机过程的转折点。 这个复合过程会演化到转点之前的一步。 布朗州变形游戏是根据这个新过程构建的, 以找到最佳的行动时刻。 通过使用波动理论和混合战略游戏理论, 取得了分析可移植的结果。 改变布朗州变体过程的联合功能是用来转换第一个穿越时间及其索引的。 这些结果使我们能够预测一个转折点的时刻和获得游戏最佳报酬的行动时刻。 这一研究调整了理论框架, 以对包括股票和网络证券在内的价值资产进行自主交易。
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