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}
}

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References

SHOWING 1-10 OF 51 REFERENCES
A new integral equation for the evaluation of first-passage-time probability densities
The first-passage-time p.d.f. through a time-dependent boundary for one-dimensional diffusion processes is proved to satisfy a new Volterra integral equation of the second kind involving two
First-passage densities of a two-dimensional process
The two-dimensional stochastic process$( x( t ),y( t ) )$, where $y( t ) = dx ( t )/dt$ is a Wiener process (Brownian motion) is considered. The value of$x( t )$ when $y( t )$ first hits a line in
First Passage Time Distribution of a Two-Dimensional Wiener Process with Drift
The two-dimensional correlated Wiener process (or Brownian motion) with drift is considered. The Fokker-Planck (or Kolmogorov forward) equation for the Wiener process (X1(t), X2(t)) is solved under
Joint Densities of First Hitting Times of a Diffusion Process Through Two Time-Dependent Boundaries
Consider a one-dimensional diffusion process on the diffusion interval I originated in x 0 ∈ I. Let a(t) and b(t) be two continuous functions of t, t > t 0, with bounded derivatives, a(t) < b(t), and
First-passage problems for degenerate two-dimensional diffusion processes
LetY(t) be a one-dimensional diffusion process anddX(t)=Y(t)dt. The process (X(t), Y(t)) is considered in the second quadrant. First, the probability that (X(t), Y(t)) will hit thex-axis before
On the first passage problem for correlated Brownian motion
One-Dimensional Homogeneous Diffusions
When constructing a model defined by a stochastic differential equation (SDE) the basic problem is whether the equation has a solution and if so, when an initial condition is given, whether the
...
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