A Way of Thinking about Depression Symptoms using the Law of Rare Events
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Until now, stochastic differential equations have been used to explain the process that leads to feelings and ideas based on the assumption of Wiener processes. In reality, however, depressive symptoms may suddenly appear when one is at ease. When a person is suffering from depression, the value of the person's similarity curve and other curve groups are at a negative minimum if we consider the Wiener process. However, a person may go from being at ease to being depressed, i.e., the value of the similarity curve or other curve group may suddenly go from a positive value to a negative minimum. Therefore, we considered depressive symptoms using the probability distributions of depressive symptom interval and frequency. First, we derived the equation used in previous papers from a one-dimensional random walk using the law of large numbers, and then derived the equation used in this paper using the law of rare events. From the derived equation, we derived a stochastic process for the frequency of depressive symptoms and the probability distributions of depressive symptom interval and frequency. Based on the derived probability distributions, we discussed possible implications for depression and proposed coping strategies. These strategies are consistent with psychiatric treatments and provide a logical basis for such interventions.
