scholarly journals Least squares estimation for path-distribution dependent stochastic differential equations

2021 ◽  
Vol 410 ◽  
pp. 126457
Author(s):  
Panpan Ren ◽  
Jiang-Lun Wu
Keyword(s):  
Differential Equations ◽  
Least Squares ◽  
Stochastic Differential Equations ◽  
Least Squares Estimation

Least Squares Estimation in Uncertain Differential Equations

2020 ◽  
Vol 28 (10) ◽  
pp. 2651-2655 ◽  
Author(s):  
Yuhong Sheng ◽  
Kai Yao ◽  
Xiaowei Chen
Keyword(s):  
Differential Equations ◽  
Least Squares ◽  
Least Squares Estimation

A second-order discretization for forward-backward SDEs using local approximations with Malliavin calculus

2019 ◽  
Vol 25 (4) ◽  
pp. 341-361
Author(s):  
Riu Naito ◽  
Toshihiro Yamada
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Differential Equations ◽  
Least Squares ◽  
Stochastic Differential Equations ◽  
Malliavin Calculus ◽  
Second Order ◽  
Discretization Method ◽  
Local Approximations ◽  
Backward Sdes

Abstract The paper proposes a new second-order discretization method for forward-backward stochastic differential equations. The method is given by an algorithm with polynomials of Brownian motions where the local approximations using Malliavin calculus play a role. For the implementation, we introduce a new least squares Monte Carlo method for the scheme. A numerical example is illustrated to check the effectiveness.

scholarly journals Statistical Inference for Stochastic Differential Equations with Small Noises

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Liang Shen ◽  
Qingsong Xu
Keyword(s):  
Differential Equations ◽  
Normal Distribution ◽  
Least Squares ◽  
Stochastic Differential Equations ◽  
Asymptotic Distribution ◽  
Asymptotic Property ◽  
Stable Distribution ◽  
Least Squares Method ◽  
Regularity Conditions ◽  
Drift Parameter

This paper proposes the least squares method to estimate the drift parameter for the stochastic differential equations driven by small noises, which is more general than pure jumpα-stable noises. The asymptotic property of this least squares estimator is studied under some regularity conditions. The asymptotic distribution of the estimator is shown to be the convolution of a stable distribution and a normal distribution, which is completely different from the classical cases.

Least squares estimation of high-order uncertain differential equations

2021 ◽  
pp. 1-10
Author(s):  
Jing Zhang ◽  
Yuhong Sheng ◽  
Xiaoli Wang
Keyword(s):  
Differential Equations ◽  
Least Squares ◽  
Estimation Method ◽  
Sum Of Squares ◽  
High Order ◽  
Least Squares Estimation ◽  
Uncertain Differential Equation ◽  
Diffusion Term ◽  
First Order ◽  
Liu Process

Parameter estimation of high-order uncertain differential equations is an inevitable problem in practice. In this paper, the equivalent equations of high-order uncertain differential equations are obtained by transformation, and the parameters of the first-order uncertain differential equation including Liu process are estimated. Based on the least squares estimation method, this paper proposes a means to minimize the residual sum of squares to obtain an estimate of the parameters in the drift term, and make the noise sum of squares equal to the residual sum of squares to obtain an estimate of the parameters in the diffusion term. In addition, some numerical examples are given to illustrate the proposed method. Finally, applications of the high-order uncertain spring vibration equations verify the viability of our method.

Least squares estimator for stochastic differential equations driven by small fractional Lévy noises from discrete observations

2021 ◽  
pp. 2150047
Author(s):  
Qian Yu ◽  
Guangjun Shen ◽  
Wentao Xu
Keyword(s):  
Asymptotic Behavior ◽  
Parameter Estimation ◽  
Differential Equations ◽  
Least Squares ◽  
Stochastic Differential Equations ◽  
Dispersion Coefficient ◽  
Least Squares Estimator ◽  
Regularity Conditions ◽  
Discrete Observations ◽  
Small Dispersion

In this paper, we consider the problem of parameter estimation for stochastic differential equations with small fractional Lévy noises, based on discrete observations. Under certain regularity conditions on drift function, the consistency of least squares estimation has been established as a small dispersion coefficient [Formula: see text] and the number of discrete points [Formula: see text] simultaneously. We also obtain the asymptotic behavior of the estimator.

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