Persistence probabilities of MA(1) sequences with Laplace innovations and q-deformed zigzag numbers

2025/12/16 by Frank Aurzada, Aurzada, Frank, Kilian Raschel +1
Mathematics · Physics and Astronomy · #Benford’s Law and Fraud Detection #Statistical Mechanics and Entropy #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.2512.14152

Abstract

We study the persistence probabilities of a moving average process of order one with innovations that follow a Laplace distribution. The persistence probabilities can be computed fully explicitly in terms of classical combinatorial quantities like certain q-Pochhammer symbols or q-deformed analogues of Euler's zigzag numbers, respectively. Similarly, the generating functions of the persistence probabilities can be written in terms of q-analogues of the exponential function or the q-sine/q-cosine functions, respectively.

Citations

• Persistence probabilities for MA(1) sequences with uniform innovations
• Persistence of AR(1) sequences with Rademacher innovations and linear mod 1 transforms
• Persistence for a class of order-one autoregressive processes and Mallows-Riordan polynomials
• Persistence exponents in Markov chains
• Persistence probabilities in centered, stationary, Gaussian processes in discrete time
• Persistence and first-passage properties in nonequilibrium systems
• Survival probabilities of autoregressive processes
• A Survey of Alternating Permutations
• Walks with small steps in the quarter plane
• Martingales and first passage times of AR(1) sequences

Related

• Persistence probabilities for MA(1) sequences with uniform innovations
• Persistence for a class of order-one autoregressive processes and Mallows-Riordan polynomials
• Persistence exponents via perturbation theory: MA(1)-processes
• Persistence probabilities & exponents
• Persistence of AR(1) sequences with Rademacher innovations and linear mod 1 transforms