Optimal Stochastic Restart Renders Fluctuations in First Passage Times Universal

Stochastic coagulation and fragmentation: incommensurability and first passage times

We develop a fully stochastic theory for coagulation and fragmentation in a finite system with a maximum cluster size constraint. The process is modeled using a high-dimensional Master equation for the probabilities of cluster configurations. For certain realizations of total mass and maximum cluster sizes, we are able to find exact analytical results for the expected equilibrium cluster distri...

First Passage times in Biology: Approximations

First-passage times of regime switching models

The probability of a stochastic process to first breach an upper and/or a lower level is an important quantity for optimal control and risk management. We present those probabilities for regime switching Brownian motion. In the 2and 3-state model, the Laplace transform of the (single and double barrier) first-passage times is – up to the roots of a polynomial of degree 4 (respectively 6) – deri...

First Passage Times, Lifetimes, and Relaxation Times of Unfolded Proteins.

The dynamics of proteins in the unfolded state can be quantified in computer simulations by calculating a spectrum of relaxation times which describes the time scales over which the population fluctuations decay to equilibrium. If the unfolded state space is discretized, we can evaluate the relaxation time of each state. We derive a simple relation that shows the mean first passage time to any ...

First-passage times in integrate-and-fire neurons with stochastic thresholds.

We consider a leaky integrate-and-fire neuron with deterministic subthreshold dynamics and a firing threshold that evolves as an Ornstein-Uhlenbeck process. The formulation of this minimal model is motivated by the experimentally observed widespread variation of neural firing thresholds. We show numerically that the mean first-passage time can depend nonmonotonically on the noise amplitude. For...