条件扩散的正反向随机表示的模拟
Simulation of forward-reverse stochastic representations for conditional diffusions
摘要：
在本文中，我们推导出有限维分布的多维扩散在一个固定的时间间隔，条件下的终态的随机表示。调节可以相对于不动点或更一般地相对于某个子集。这些表示依赖于与给定（前向）扩散相关的反向过程，如Milstein，Schoenmakers和Spokoiny [Bernoulli 10（2004）281-312]在前向-反向转移密度估计器的上下文中所介绍的。相应的蒙特卡罗估计基本上具有根- $N$精度，因此它们不受维数灾难的影响。我们提供了一个详细的收敛性分析，并给出了一个数值例子，涉及实现方差的随机波动率资产模型的条件下，固定的终端价值的资产。
英文摘要：
In this paper we derive stochastic representations for the finite dimensional distributions of a multidimensional diffusion on a fixed time interval, conditioned on the terminal state. The conditioning can be with respect to a fixed point or more generally with respect to some subset. The representations rely on a reverse process connected with the given (forward) diffusion as introduced in Milstein, Schoenmakers and Spokoiny [Bernoulli 10 (2004) 281-312] in the context of a forward-reverse transition density estimator. The corresponding Monte Carlo estimators have essentially root-$N$ accuracy, and hence they do not suffer from the curse of dimensionality. We provide a detailed convergence analysis and give a numerical example involving the realized variance in a stochastic volatility asset model conditioned on a fixed terminal value of the asset.
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