One Dimensional Stochastic Differential Equations with No Strong Solution

1982 ◽  
Vol s2-26 (2) ◽  
pp. 335-347 ◽  
Author(s):  
M. T. Barlow
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Strong Solution ◽  
One Dimensional

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]

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
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