Second-order weak approximations for stratonovich stochastic differential equations

1994 ◽  
Vol 34 (2) ◽  
pp. 183-200 ◽  
Author(s):  
V. Mackevičius
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Second Order ◽  
Weak Approximations

scholarly journals On positive approximations of positive diffusions

2007 ◽  
Vol 47 ◽  
Author(s):  
Vigirdas Mackevičius
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Second Order ◽  
Positivity Property ◽  
Weak Approximations

For positive diffusions, we construct split-step second-order weak approximations preserving the positivity property. For illustration, we apply the construction to some popular stochastic differential equations such as Verhulst, CIR, and CKLS equations.

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.

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