First passage time distribution of active thermal particles in potentials

Run-and-tumble motion in a harmonic potential: field theory and entropy production

“…with eigenvalue λ n = −n/L 2 , where H n (x) is the nth Hermite polynomial in the 'probabilists' convention', see appendix B [35,[42][43][44]. The functions u n (x) are similar to the so-called Hermite functions exp(−x 2 /(4L 2 )) H n (x/L).…”

Noise can lead to exponential epidemic spreading despite $R_0$ below one

“…The dimensionless parameter λ is the coupling strength and β is the return rate. The persistence time β −1 induces temporal correlations, or a memory, in the noise y(t) in a similar way to active fluctuations in the motion of active Ornstein-Uhlenbeck particles [33,34], Eq. (18).…”

Field theory of survival probabilities, extreme values, first passage times, and mean span of non-Markovian stochastic processes

“…In our recent work [26], we presented a scheme to calculate first-passage distributions for the same class of * bwalter@sissa.it non-Markovian processes. These results relied on a perturbative functional expansion of a renewal type equation inspired by the classical work of [10,27].…”

“…Example: Brownian Motion driven by self-correlated noise-We briefly discuss the example process of active thermal Brownian motion (ATBM, [26]) on a real line. In our previous article [26], we found the perturbative correction to the first-passage time moment generating function for an active thermal Ornstein Uhlenbeck process, and an active Brownian Motion on a ring.…”

“…Example: Brownian Motion driven by self-correlated noise-We briefly discuss the example process of active thermal Brownian motion (ATBM, [26]) on a real line. In our previous article [26], we found the perturbative correction to the first-passage time moment generating function for an active thermal Ornstein Uhlenbeck process, and an active Brownian Motion on a ring. Since the distribution of first-passage times and visits are closely linked via Q(x, ω) = (−iω) −1 χ FPT (x, ω), we report the visit probabilities of the latter two processes in App.…”