L-operator integro-differential inequality for dissipativity of stochastic integro-differential equations

L–operator Integro–differential Inequality for Dissipativity of Stochastic Integro–differential Equations

In this paper, Itô stochastic integro-differential equations are considered. By establishing an L -operator integro-differential inequality and using the properties of M -cone and stochastic analysis technique, we obtain some new sufficient conditions ensuring the exponential p -dissipativity of the stochastic integro-differential equations. An example is also discussed to illustrate the effici...

Integro - Differential Stochastic Resonance

A new class of stochastic resonator (SRT) and Stochastic Resonance (SR) phenomena are described. The new SRT consist of a classical SRT, one or more time derivative circuits and the same number of time integrators. The incoming signal with additive noise is first time derivated, then passes through the classical SRT and finally it is time integrated. The resulting SR phenomena show a well defin...

Nonlinear Integro - Differential Equations

Some identification problems for integro - differential operator equations ∗

We consider, in a Hilbert space H, the convolution integro-differential equation u′′(t)−h∗Au(t) = f(t), 0 ≤ t ≤ T , h∗v(t) = ∫ t 0 h(t−s)v(s) ds, where A is a linear closed densely defined (possibly selfadjoint and/or positive definite) operator in H. Under suitable assumptions on the data we solve the inverse problem consisting of finding the kernel h from the extra data (measured data) of the...

Stochastic Homogenization for Some Nonlinear Integro-Differential Equations

In this note we prove the stochastic homogenization for a large class of fully nonlinear elliptic integro-differential equations in stationary ergodic random environments. Such equations include, but are not limited to Bellman equations and the Isaacs equations for the control and differential games of some pure jump processes in a random, rapidly varying environment. The translation invariant ...