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]

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 Strong Solution Existence for a Class of Degenerate Stochastic Differential Equations

2020 ◽  
Vol 53 (2) ◽  
pp. 2220-2224
Author(s):  
William M. McEneaney ◽  
Hidehiro Kaise ◽  
Peter M. Dower ◽  
Ruobing Zhao
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Strong Solution ◽  
Solution Existence

Stability of stochastic differential equations driven by multifractional Brownian motion

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Oussama El Barrimi ◽  
Youssef Ouknine
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Stationary Process ◽  
Strong Stability ◽  
Pathwise Uniqueness ◽  
Uniqueness Property ◽  
Selection Theorem ◽  
Multifractional Brownian Motion ◽  
Stability Results

Abstract Our aim in this paper is to establish some strong stability results for solutions of stochastic differential equations driven by a Riemann–Liouville multifractional Brownian motion. The latter is defined as a Gaussian non-stationary process with a Hurst parameter as a function of time. The results are obtained assuming that the pathwise uniqueness property holds and using Skorokhod’s selection theorem.

2D Self-assembly and Electronic Characterization of Oxygen-Boron-Oxygen-Doped Chiral Graphene Nanoribbons

2021 ◽  
Author(s):  
Lei Jin ◽  
Nerea Bilbao ◽  
Yang Lv ◽  
Xiao-Ye Wang ◽  
Soltani Paniz ◽  
...  
Keyword(s):  
Edge Effects ◽  
Self Assembly ◽  
Quantum Confinement ◽  
Graphene Nanoribbons ◽  
One Dimensional ◽  
The Past ◽  
Different Types

Graphene nanoribbons (GNRs), quasi-one-dimensional strips of graphene, exhibit a nonzero bandgap due to quantum confinement and edge effects. In the past decade, different types of GNRs with atomically precise structures...

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