Unbiased simulation of stochastic differential equations using parametrix expansions
نویسنده
چکیده
We consider an unbiased simulation method for multidimensional diffusions based on the parametrix method for solving partial differential equations with H’́older continuous coefficients. This Monte Carlo method which is based on an Euler scheme with random time steps, can be considered as an infinite dimensional extension of the Multilevel Monte Carlo method for solutions of stochastic differential equations with H’́older continuous coefficients. In particular, we study the properties of the variance of the proposed method. In most cases, the method has infinite variance and therefore we propose an importance sampling method to resolve this issue. ∗Speaker sciencesconf.org:montecarlo16:111508
منابع مشابه
A probabilistic interpretation of the parametrix method
In this article, we introduce the parametrix method for constructions of fundamental solutions as a general method based on semigroups and difference of generators. This leads to a probabilistic interpretation of the parametrix method that are amenable to Monte Carlo simulation. We consider the explicit examples of continuous diffusions and jump driven stochastic differential equations with Höl...
متن کاملUnbiased simulation of stochastic differential equations
We propose an unbiased Monte-Carlo estimator for E[g(X t1,,X tn)], where X is a diffusion process defined by a multi-dimensional stochastic differential equation (SDE). The main idea is to start instead from a well-chosen simulatable SDE whose coefficients are updated at independent exponential times. Such a simulatable process can be viewed as a regimeswitching SDE, or as a branching diffusion...
متن کاملNumerical solution and simulation of random differential equations with Wiener and compound Poisson Processes
Ordinary differential equations(ODEs) with stochastic processes in their vector field, have lots of applications in science and engineering. The main purpose of this article is to investigate the numerical methods for ODEs with Wiener and Compound Poisson processes in more than one dimension. Ordinary differential equations with Ito diffusion which is a solution of an Ito stochastic differentia...
متن کاملSimulating and Forecasting OPEC Oil Price Using Stochastic Differential Equations
The main purpose of this paper is to provide a quantitative analysis to investigate the behavior of the OPEC oil price. Obtaining the best mathematical equation to describe the price and volatility of oil has a great importance. Stochastic differential equations are one of the best models to determine the oil price, because they include the random factor which can apply the effect of different ...
متن کاملSolving Differential Equations Using Modified VIM
In this paper a modification of He's variational iteration method (VIM) has been employed to solve Dung and Riccati equations. Sometimes, it is not easy or even impossible, to obtain the first few iterations of VIM, therefore, we suggest to approximate the integrand by using suitable expansions such as Taylor or Chebyshev expansions.
متن کامل