Representation of Semimartingale Markov Processes in Terms of Wiener Processes and Poisson Random Measures

1981 ◽  
pp. 159-242 ◽  
Author(s):  
E. Çinlar ◽  
J. Jacod
Keyword(s):  
Markov Processes ◽  
Random Measures ◽  
Poisson Random Measures ◽  
Wiener Processes

scholarly journals Some Refinements of Existence Results for SPDEs Driven by Wiener Processes and Poisson Random Measures

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Stefan Tappe
Keyword(s):  
Existence And Uniqueness ◽  
Linear Growth ◽  
Mild Solutions ◽  
Existence Results ◽  
Moving Frame ◽  
Local Boundedness ◽  
Random Measures ◽  
Poisson Random Measures ◽  
Wiener Processes ◽  
Global And Local

We provide existence and uniqueness of global (and local) mild solutions for a general class of semilinear stochastic partial differential equations driven by Wiener processes and Poisson random measures under local Lipschitz and linear growth (or local boundedness, resp.) conditions. The so-called “method of the moving frame” allows us to reduce the SPDE problems to SDE problems.

scholarly journals On Itô formulas for jump processes

2021 ◽  
Author(s):  
István Gyöngy ◽  
Sizhou Wu
Keyword(s):  
Jump Processes ◽  
Stochastic Pdes ◽  
Stochastic Integrals ◽  
Itô Formula ◽  
Random Measures ◽  
Ito Formula ◽  
Poisson Random Measures ◽  
Infinite Dimensional ◽  
Wiener Processes ◽  
Finite Dimensional

AbstractA well-known Itô formula for finite-dimensional processes, given in terms of stochastic integrals with respect to Wiener processes and Poisson random measures, is revisited and is revised. The revised formula, which corresponds to the classical Itô formula for semimartingales with jumps, is then used to obtain a generalisation of an important infinite-dimensional Itô formula for continuous semimartingales from Krylov (Probab Theory Relat Fields 147:583–605, 2010) to a class of $$L_p$$ L p -valued jump processes. This generalisation is motivated by applications in the theory of stochastic PDEs.

Stochastic Cahn-Hilliard equations driven by Poisson random measures

2014 ◽  
Vol 57 (12) ◽  
pp. 2563-2576
Author(s):  
YiMing Jiang ◽  
KeHua Shi ◽  
SuXin Wang
Keyword(s):  
Random Measures ◽  
Poisson Random Measures
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