Stabilization of Partial Differential Equations by Levy Noise
Jianhai Bao, Chenggui Yuan
TL;DR
This paper investigates how Levy noise can be used to stabilize partial differential equations, providing conditions for exponential decay and demonstrating applications through examples.
Contribution
It introduces new sufficient conditions for the exponential stabilization of PDEs using Levy noise, expanding the understanding of stochastic control in infinite-dimensional systems.
Findings
Provided conditions for exponential decay of PDEs under Levy noise
Constructed examples demonstrating the application of the stabilization theory
Extended stochastic stabilization techniques to systems driven by Levy processes
Abstract
We focus in this paper on the stochastic stabilization problems of PDEs by Levy noise. Sufficient conditions under which the perturbed systems decay exponentially with a general rate function are provided and some examples are constructed to demonstrate the applications of our theory.
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Taxonomy
TopicsStochastic processes and financial applications · Stability and Controllability of Differential Equations · Insurance, Mortality, Demography, Risk Management