## Journal of Applied Probability

- J. Appl. Probab.
- Volume 40, Number 3 (2003), 557-580.

### Biased movement at a boundary and conditional occupancy times for diffusion processes

Otso Ovaskainen and Stephen J. Cornell

#### Abstract

Motivated by edge behaviour reported for biological organisms, we show that random walks with a bias at a boundary lead to a discontinuous probability density across the boundary. We continue by studying more general diffusion processes with such a discontinuity across an interior boundary. We show how hitting probabilities, occupancy times and conditional occupancy times may be solved from problems that are adjoint to the original diffusion problem. We highlight our results with a biologically motivated example, where we analyze the movement behaviour of an individual in a network of habitat patches surrounded by dispersal habitat.

#### Article information

**Source**

J. Appl. Probab. Volume 40, Number 3 (2003), 557-580.

**Dates**

First available in Project Euclid: 24 July 2003

**Permanent link to this document**

http://projecteuclid.org/euclid.jap/1059060888

**Digital Object Identifier**

doi:10.1239/jap/1059060888

**Mathematical Reviews number (MathSciNet)**

MR1993253

**Zentralblatt MATH identifier**

02066237

**Subjects**

Primary: 60J60: Diffusion processes [See also 58J65]

Secondary: 92D50: Animal behavior

**Keywords**

Random walk bias at boundary diffusion approximation hitting probability exit time conditional exit time occupancy time conditional occupancy time

#### Citation

Ovaskainen, Otso; Cornell, Stephen J. Biased movement at a boundary and conditional occupancy times for diffusion processes. J. Appl. Probab. 40 (2003), no. 3, 557--580. doi:10.1239/jap/1059060888. http://projecteuclid.org/euclid.jap/1059060888.