scholarly journals Estimating reducible stochastic differential equations by conversion to a least-squares problem

2018 ◽  
Vol 34 (1) ◽  
pp. 23-46 ◽  
Author(s):  
Oscar García
Keyword(s):  
Differential Equations ◽  
Least Squares ◽  
Stochastic Differential Equations ◽  
Least Squares Problem

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 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.

Stochastic Differential Equations for Power Law Behaviors

2012 ◽  
Author(s):  
Bo Jiang ◽  
Roger Brockett ◽  
Weibo Gong ◽  
Don Towsley
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Power Law
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