The way of thinking about depressive symptoms using Poisson process and exponential distribution (exponential process)

So far, we have been using stochastic differential equations to explain the process of deriving emotions and ways of thinking based on the assumption of a Wiener process. However, in reality, there are cases where depression suddenly appears when things are going well. If a person is suffering from depression, the values of the group of curves, such as the similarity curve, will be at their lowest negative value if we consider them using a Wiener process. However, there are cases where a person goes from feeling good to suffering from depression, in other words, where the values of the group of curves, such as the similarity curve, suddenly change from positive to their lowest negative value. This cannot be explained using the conventional approach of considering groups of curves such as similar curves using the Wiener process. Therefore, we considered depression symptoms using the Poisson process and the exponential distribution (exponential process). We derived a stochastic differential equation that gives the number of times a person become depressed within a certain period of time, and showed that the number of times a person become depressed within a certain period of time follows a Poisson process. We also derived a stochastic differential equation that gives the time a person is feeling depressed, and showed that the time a person is feeling depressed follows an exponential distribution (exponential process). Based on these results, we explained the relationship between the number of times a person become depressed within a certain period of time and the length of time one is depressed. We also discussed the connections with similarity curve and other topics discussed in previous papers. Finally, We stated that putting oneself in an environment or situation where one is less likely to become depressed is a way of dealing with depression.