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# A Stochastic Processes Framework for Resilience Quantification

We describe the resilience of a system as a characteristic of the temporal evolution of three of its properties: its tendency to revert to nominal performance, its sensitivity to external stressors and the expected value of the long term performance. The differentiation between resilient and non-resilient systems is made depending on whether the combined effect of these three properties decreases the probability that the performance level of the system violates a robustness range as time progresses. An example of such systems is presented, in the form of a stochastic difference equation. A family of self-hardening mean reverting processes is defined by introducing parameterizations of the mean reversion rate, long term expectation value and volatility. These parametrizations are increasing with respect to past innovations of the process - to capture learning - and temporally decreasing - to model forgetting. Finally, we explore the space defined by the three individual decay rates and assess the resilience level over the specific family of models.