scholarly journals Stochastic Integration with Respect to Cylindrical Lévy Processes by p-Summing Operators

2020 ◽  
Author(s):  
Tomasz Kosmala ◽  
Markus Riedle
Keyword(s):  
Evolution Equation ◽  
Banach Spaces ◽  
Lévy Processes ◽  
Stochastic Integral ◽  
Levy Processes ◽  
Integration Theory ◽  
Stochastic Evolution Equation ◽  
Stochastic Integration ◽  
Stochastic Evolution ◽  
Existence Of A Solution

AbstractWe introduce a stochastic integral with respect to cylindrical Lévy processes with finite p-th weak moment for $$p\in [1,2]$$p∈[1,2]. The space of integrands consists of p-summing operators between Banach spaces of martingale type p. We apply the developed integration theory to establish the existence of a solution for a stochastic evolution equation driven by a cylindrical Lévy process.

scholarly journals Integrated solutions of stochastic evolution equations with additive noise

2001 ◽  
Vol 64 (2) ◽  
pp. 281-290 ◽  
Author(s):  
A. Filinkov ◽  
I. Maizurna
Keyword(s):  
Evolution Equation ◽  
Additive Noise ◽  
Evolution Equations ◽  
Stochastic Evolution Equation ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Existence Of A Solution ◽  
Integrated Semigroup

We investigate the existence of a solution to the abstract stochastic evolution equation with additive noise: in the case when A is the generator of an n-times integrated semigroup.

scholarly journals An Inverse Problem for a Class of Linear Stochastic Evolution Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-25
Author(s):  
Yuhuan Zhao
Keyword(s):  
Inverse Problem ◽  
Evolution Equation ◽  
Evolution Equations ◽  
Optimal Parameter ◽  
Optimization Method ◽  
Necessary Condition ◽  
Stochastic Evolution Equation ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Fréchet Differentiable

An inverse problem for a linear stochastic evolution equation is researched. The stochastic evolution equation contains a parameter with values in a Hilbert space. The solution of the evolution equation depends continuously on the parameter and is Fréchet differentiable with respect to the parameter. An optimization method is provided to estimate the parameter. A sufficient condition to ensure the existence of an optimal parameter is presented, and a necessary condition that the optimal parameter, if it exists, should satisfy is also presented. Finally, two examples are given to show the applications of the above results.

scholarly journals On Jumps Stochastic Evolution Equations With Application of Homogenization and Large Deviations

2019 ◽  
Vol 11 (2) ◽  
pp. 125
Author(s):  
Cl´ement Manga ◽  
Alioune Coulibaly ◽  
Alassane Diedhiou
Keyword(s):  
Evolution Equation ◽  
Large Deviations ◽  
Evolution Equations ◽  
Stochastic Evolution Equation ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Large Deviations Principle ◽  
Viscosity Parameter ◽  
Two Parameters ◽  
And Diffusion

We consider a class of jumps and diffusion stochastic differential equations which are perturbed by to two parameters:  ε (viscosity parameter) and δ (homogenization parameter) both tending to zero. We analyse the problem taking into account the combinatorial effects of the two parameters  ε and δ . We prove a Large Deviations Principle estimate for jumps stochastic evolution equation in case that homogenization dominates.

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