scholarly journals Anticipating Stochastic Differential Equations: Regularity of the Law

1997 ◽  
Vol 143 (1) ◽  
pp. 157-179 ◽  
Author(s):  
Carles Rovira ◽  
Marta Sanz-Solé
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
The Law

scholarly journals Mean reflected stochastic differential equations with jumps

2020 ◽  
Vol 52 (2) ◽  
pp. 523-562
Author(s):  
Phillippe Briand ◽  
Abir Ghannoum ◽  
Céline Labart
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Stochastic Differential Equations ◽  
Numerical Scheme ◽  
The Law

AbstractIn this paper, a reflected stochastic differential equation (SDE) with jumps is studied for the case where the constraint acts on the law of the solution rather than on its paths. These reflected SDEs have been approximated by Briand et al. (2016) using a numerical scheme based on particles systems, when no jumps occur. The main contribution of this paper is to prove the existence and the uniqueness of the solutions to this kind of reflected SDE with jumps and to generalize the results obtained by Briand et al. (2016) to this context.

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