scholarly journals Hitting probabilities of a Brownian flow with radial drift

2020 ◽  
Vol 48 (2) ◽  
pp. 646-671
Author(s):  
Jong Jun Lee ◽  
Carl Mueller ◽  
Eyal Neuman
Keyword(s):  
Hitting Probabilities

scholarly journals Markov chains with quasitoeplitz transition matrix: first zero hitting

1989 ◽  
Vol 2 (3) ◽  
pp. 205-216
Author(s):  
Alexander M. Dukhovny
Keyword(s):  
Markov Chains ◽  
Boundary Value Problems ◽  
Unit Circle ◽  
Generating Functions ◽  
Transition Matrix ◽  
Boundary Value ◽  
Riemann Boundary ◽  
Hitting Probabilities

This paper continues the investigation of Markov Chains with a quasitoeplitz transition matrix. Generating functions of first zero hitting probabilities and mean times are found by the solution of special Riemann boundary value problems on the unit circle. Duality is discussed.

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

2003 ◽  
Vol 40 (3) ◽  
pp. 557-580 ◽  
Author(s):  
Otso Ovaskainen ◽  
Stephen J. Cornell
Keyword(s):  
Random Walks ◽  
Probability Density ◽  
Diffusion Processes ◽  
Diffusion Problem ◽  
Movement Behaviour ◽  
Habitat Patches ◽  
Hitting Probabilities ◽  
Interior Boundary ◽  
Biological Organisms

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.

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

2003 ◽  
Vol 40 (03) ◽  
pp. 557-580 ◽  
Author(s):  
Otso Ovaskainen ◽  
Stephen J. Cornell
Keyword(s):  
Random Walks ◽  
Probability Density ◽  
Diffusion Processes ◽  
Diffusion Problem ◽  
Movement Behaviour ◽  
Habitat Patches ◽  
Hitting Probabilities ◽  
Interior Boundary ◽  
Biological Organisms

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.

Sign in / Sign up

Export Citation Format

Share Document