Multidimensional compound Poisson approximations for symmetric distributions

Key Points

• The study aims to approximate the distribution of sums of independent symmetric lattice vectors using compound Poisson laws.
• Constructed Bergström-type asymptotic expansion for approximations.
• Evaluated approximation accuracy using total variation metric.
• Estimated the error order as O(n^-1) in specific cases.
• Developed a compound Poisson law for independent symmetric lattice vector sums.
• Achieved accuracy of approximation in total variation metric at order O(n^-1).