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We consider the motion of an active Brownian particle with speed fluctuationsin d-dimensions in the presence of both translational and orientationaldiffusion. We use an Ornstein-Uhlenbeck process for active speed generation.Using a Laplace transform approach, we describe and use a Fokker-Planckequation-based method to evaluate the exact time dependence of all relevantdynamical moments. We present explicit calculations of such moments and compareour analytical predictions against numerical simulations to demonstrate andanalyze several dynamical crossovers. The kurtosis of displacement showspositive or negative deviations from a Gaussian behavior at intermediate timesdepending on the dominance of speed or orientational fluctuations.

Active Brownian motion with speed fluctuations in arbitrary dimensions: exact calculation of moments and dynamical crossovers