Abstract
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.
Highlights
Let ε, δ > 0, we consider the following stochastic differential equations (SDE) : Xtx,ε,δ − x = √ ε ∫t σ ( Xsx,ε,δ δ ) dWs + ε δ ∫t b ds ∫t c Ltε,δ
We consider a class of jumps and diffusion stochastic differential equations which are perturbed by two parameters: ε and δ both tending to zero
We prove a Large Deviations Principle estimate for jumps stochastic evolution equation in case that homogenization dominates
Summary
For Brownian functional with combinatorial effect of LDP and Homogenization theory, Freidlin and Sowers, 1999, have shown three classical regimes depending on the relative rate at which the small viscosity parameter ε and the homogenization parameter δ tend to zero. They have proved some Large Deviations estimates which are very effective for SDE. There are still few results on the large deviation for stochastic evolution equations with Poisson jumps (see for example, Rockner & Zang, 2007). In Section (3) we state the main result and give its proof
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
