Variance of particle location in the stochastic model of PSO with inertia weight

In the Particle Swarm Optimization (PSO) method, the behavior of particles depends on movement parameters. Effective application of the PSO method in real-world problems requires stable behavior of particles in the swarm. In the stochastic particle stability analysis, recurrent formulas of expected value and variance of particle location are used. An explicit formula for the variance can also be obtained, however, it cannot be applied in practice due to its complexity. In our research, we propose assumptions guaranteeing a simple explicit formula for location variance. For the formula and given assumptions, we show stability areas in the particle configuration space, which guarantee order-2* stability of particles also for probability distributions of movement parameters other than uniform. The areas are verified in simulations.