# First passage times of two-dimensional correlated processes: Analytical results for the Wiener process and a numerical method for diffusion processes

@article{Sacerdote2016FirstPT, title={First passage times of two-dimensional correlated processes: Analytical results for the Wiener process and a numerical method for diffusion processes}, author={Laura Sacerdote and Massimiliano Tamborrino and Cristina Zucca}, journal={J. Comput. Appl. Math.}, year={2016}, volume={296}, pages={275-292} }

## 16 Citations

Exact Simulation of the First-Passage Time of Diffusions

- MathematicsJ. Sci. Comput.
- 2019

A new rejection sampling algorithm is introduced which permits to perform an exact simulation of the first-passage time for general one-dimensional diffusion processes and is essentially based on Girsanov's transformation.

Time interval of multiple crossings of the Wiener process and a fixed threshold in engineering

- Computer Science, Mathematics
- 2020

Family of closed-form solutions for two-dimensional correlated diffusion processes.

- MathematicsPhysical review. E
- 2019

This paper studied two-dimensional, time-homogeneous, spatially correlated diffusion with linear, axis-aligned, absorbing boundaries and found that such solutions can be built if and only if the correlation coefficient ρ between the two diffusing processes takes one of a numerable set of values.

A Symmetry-Based Approach for First-Passage-Times of Gauss-Markov Processes through Daniels-Type Boundaries

- MathematicsSymmetry
- 2020

The main results of this paper are the alternative proofs to characterize the transition probability density between the two boundaries and the first passage time density exploiting exclusively symmetry properties.

Approximation of the first passage time density of a Wiener process to an exponentially decaying boundary by two-piecewise linear threshold. Application to neuronal spiking activity.

- MathematicsMathematical biosciences and engineering : MBE
- 2016

A Brownian motion in presence of an exponentially decaying threshold to model the neuronal spiking activity is considered and theoretical means, variances and coefficients of variation given by the method are compared with empirical quantities from simulated data.

Asymptotics of Two-boundary First-exit-time Densities for Gauss-Markov Processes

- Mathematics
- 2018

The problem of escape times from a region confined by two time-dependent boundaries is considered for a class of Gauss-Markov processes. Asymptotic approximations of the first exit time probability…

First passage time and statistical thermodynamics

- Physics
- 2021

The first-passage time is proposed as an independent thermodynamic parameter of the statistical distribution that generalizes the Gibbs distribution. The theory does not include the determination of…

On the exit time from open sets of some semi-Markov processes

- MathematicsThe Annals of Applied Probability
- 2020

In this paper we characterize the distribution of the first exit time from an arbitrary open set for a class of semi-Markov processes obtained as time-changed Markov processes. We estimate the…

Bi-Directional Grid Constrained Stochastic Processes' Link to Multi-Skew Brownian Motion

- Computer Science
- 2021

It is identified that BGCSPs are a variant rather than a special case of the multi-skew Brownian motion (M-SBM), which has their own complexities, such as the barriers being hidden (not known in advance) and not necessarily constant over time.

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