## References

SHOWING 1-10 OF 48 REFERENCES

### First-passage times of two-dimensional Brownian motion

- MathematicsAdvances in Applied Probability
- 2016

Abstract First-passage times (FPTs) of two-dimensional Brownian motion have many applications in quantitative finance. However, despite various attempts since the 1960s, there are few analytical…

### Hitting time for correlated three-dimensional Brownian motion

- Mathematics
- 2013

Let X = (X1;X2;X3) be a three-dimensional correlated Brownian motion and T i be the first hitting time of a fixed level by Xi. The purpose of this paper is to compute the joint density of T = inf(T1,…

### Reflected Brownian motion in a wedge: sum-of-exponential stationary densities

- Mathematics
- 2007

We give necessary and sufficient conditions for the stationary density of semimartingale reflected Brownian motion in a wedge to be written as a finite sum of terms of exponential product form.…

### REFLECTED ON BROWNIAN MOTION

- Mathematics
- 2005

We study Brownian motion reflected on an “independent” Brownian path. We prove results on the joint distribution of both processes and the support of the parabolic measure in the space-time domain…

### Hitting Lines with Two-Dimensional Brownian Motion

- Mathematics
- 1985

We use a simple model for the spontaneous activity of two neurons to arrive at a correlated two-dimensional Brownian motion, $( X_1 ( t ),X_2 ( t ) )$. We then compute the joint distribution of $\tau…

### A Random Walk on Rectangles Algorithm

- Mathematics
- 2006

In this article, we introduce an algorithm that simulates efficiently the first exit time and position from a rectangle (or a parallelepiped) for a Brownian motion that starts at any point inside.…

### A guide to Brownian motion and related stochastic processes

- Mathematics
- 2018

This is a guide to the mathematical theory of Brownian motion and related stochastic processes, with indications of how this theory is related to other branches of mathematics, most notably the…

### Three dimensional distribution of Brownian motion extrema

- Mathematics
- 2013

This paper describes the joint distributions of minima, maxima and endpoint values for a three dimensional (3D) Wiener process. In particular, the results provide the joint cumulative distributions…