On representations of solutions of 1–dimensional stochastic differential equations with reflecting boundary conditions

1987 ◽  
Vol 5 (2) ◽  
pp. 167-188
Author(s):  
Jai Heui Kim
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Stochastic Differential Equations

scholarly journals Maximum principles for nonlocal parabolic Waldenfels operators

2019 ◽  
Vol 09 (03) ◽  
pp. 1950015 ◽  
Author(s):  
Qiao Huang ◽  
Jinqiao Duan ◽  
Jiang-Lun Wu
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Stochastic Differential Equations ◽  
Markov Processes ◽  
Parabolic Equations ◽  
Lévy Processes ◽  
Stochastic Dynamics ◽  
Levy Processes ◽  
Maximum Principles

As a class of Lévy type Markov generators, nonlocal Waldenfels operators appear naturally in the context of investigating stochastic dynamics under Lévy fluctuations and constructing Markov processes with boundary conditions (in particular the construction with jumps). This work is devoted to prove the weak and strong maximum principles for ‘parabolic’ equations with nonlocal Waldenfels operators. Applications in stochastic differential equations with [Formula: see text]-stable Lévy processes are presented to illustrate the maximum principles.

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