Absolute continuity of the laws of one-dimensional reflected stochastic differential equations involving the maximum process

2021 ◽  
Vol 495 (1) ◽  
pp. 124692
Author(s):  
Hua Zhang
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Absolute Continuity ◽  
One Dimensional ◽  
Maximum Process

Approximation of Euler–Maruyama for one-dimensional stochastic differential equations involving the maximum process

2020 ◽  
Vol 26 (1) ◽  
pp. 33-47
Author(s):  
Kamal Hiderah
Keyword(s):  
Differential Equations ◽  
Strong Convergence ◽  
Stochastic Differential Equations ◽  
Diffusion Coefficients ◽  
One Dimensional ◽  
Maximum Process ◽  
And Diffusion

AbstractThe aim of this paper is to show the approximation of Euler–Maruyama {X_{t}^{n}} for one-dimensional stochastic differential equations involving the maximum process. In addition to that it proves the strong convergence of the Euler–Maruyama whose both drift and diffusion coefficients are Lipschitz. After that, it generalizes to the non-Lipschitz case.

scholarly journals ON ONE-DIMENSIONAL STOCHASTIC DIFFERENTIAL EQUATIONS INVOLVING THE MAXIMUM PROCESS

2009 ◽  
Vol 09 (02) ◽  
pp. 277-292 ◽  
Author(s):  
R. BELFADLI ◽  
S. HAMADÈNE ◽  
Y. OUKNINE
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Strong Solution ◽  
Pathwise Uniqueness ◽  
One Dimensional ◽  
The Third ◽  
The Past ◽  
Uniqueness Results ◽  
Maximum Process ◽  
Different Types

We prove existence and pathwise uniqueness results for four different types of stochastic differential equations (SDEs) perturbed by the past maximum process and/or the local time at zero. Along the first three studies, the coefficients are no longer Lipschitz. The first type is the equation [Formula: see text] The second type is the equation [Formula: see text] The third type is the equation [Formula: see text] We end the paper by establishing the existence of strong solution and pathwise uniqueness, under Lipschitz condition, for the SDE [Formula: see text]

Comparison Theorem for any Solutions of Backward Stochastic Differential Equations and its Application

2012 ◽  
Vol 524-527 ◽  
pp. 3801-3804
Author(s):  
Shi Yu Li ◽  
Wu Jun Gao ◽  
Jin Hui Wang
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Comparison Theorem ◽  
Backward Stochastic Differential Equations ◽  
Stochastic Equations ◽  
Local Martingale ◽  
One Dimensional ◽  
Lipschitz Continuous ◽  
The One ◽  
Uniformly Lipschitz

ƒIn this paper, we study the one-dimensional backward stochastic equations driven by continuous local martingale. We establish a generalized the comparison theorem for any solutions where the coefficient is uniformly Lipschitz continuous in z and is equi-continuous in y.

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