论文标题
Yoccoz-Birkeland牲畜种群模型和随机价格动态
The Yoccoz-Birkeland livestock population model coupled with random price dynamics
论文作者
论文摘要
我们研究了Arlot，Marmi和Papini在Arlot等人中提出的人口市场模型的随机版本。 （2019）。后一个模型基于Yoccoz-Birkeland的积分方程，并描述了表现出内源性确定性随机行为的牲畜商品价格的时间演变。我们将来自黑色choles市场模型启发的随机组件介绍到价格方程式中，并证明存在随机吸引子和随机不变的度量。我们以数值计算分形维度和随机吸引子的熵，并显示其与确定性的趋势，因为市场方程中的波动率往往为零。我们还详细研究了吸引子对时间消化参数的选择的依赖性。我们实施了几个统计距离，以量化离散系统吸引子与原始系统的相似性。特别是，在Cuturi（2013）的工作之后，我们使用了凹痕距离。考虑到运输成本矩阵，这是两种措施之间的最佳运输距离的离散版本。
We study a random version of the population-market model proposed by Arlot, Marmi and Papini in Arlot et al. (2019). The latter model is based on the Yoccoz-Birkeland integral equation and describes a time evolution of livestock commodities prices which exhibits endogenous deterministic stochastic behaviour. We introduce a stochastic component inspired from the Black-Scholes market model into the price equation and we prove the existence of a random attractor and of a random invariant measure. We compute numerically the fractal dimension and the entropy of the random attractor and we show its convergence to the deterministic one as the volatility in the market equation tends to zero. We also investigate in detail the dependence of the attractor on the choice of the time-discretization parameter. We implement several statistical distances to quantify the similarity between the attractors of the discretized systems and the original one. In particular, following a work by Cuturi (2013), we use the Sinkhorn distance. This is a discrete and penalized version of the Optimal Transport Distance between two measures, given a transport cost matrix.
