Order statistics for first passage times in one-dimensional diffusion processes

1996 ◽  
Vol 85 (3-4) ◽  
pp. 501-512 ◽  
Author(s):  
S. Bravo Yuste ◽  
Katja Lindenberg
Keyword(s):  
Order Statistics ◽  
Diffusion Processes ◽  
First Passage Times ◽  
First Passage ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Passage Times

Order statistics for first passage times in diffusion processes

1983 ◽  
Vol 31 (2) ◽  
pp. 255-278 ◽  
Author(s):  
George H. Weiss ◽  
Kurt E. Shuler ◽  
Katja Lindenberg
Keyword(s):  
Order Statistics ◽  
Diffusion Processes ◽  
First Passage Times ◽  
First Passage ◽  
Passage Times

The Level-Crossing Problem: First-Passage, Escape and Extremes

2014 ◽  
Vol 13 (04) ◽  
pp. 1430001 ◽  
Author(s):  
Jaume Masoliver
Keyword(s):  
Brownian Motion ◽  
Diffusion Processes ◽  
Extreme Values ◽  
Level Crossing ◽  
First Passage ◽  
One Dimensional ◽  
Absolute Value ◽  
Dimensional Diffusion

We review the level-crossing problem which includes the first-passage and escape problems as well as the theory of extreme values (the maximum, the minimum, the maximum absolute value and the range or span). We set the definitions and general results and apply them to one-dimensional diffusion processes with explicit results for the Brownian motion and the Ornstein–Uhlenbeck (OU) process.

First-passage-time densities for time-non-homogeneous diffusion processes

1997 ◽  
Vol 34 (3) ◽  
pp. 623-631 ◽  
Author(s):  
R. Gutiérrez ◽  
L. M. Ricciardi ◽  
P. Román ◽  
F. Torres
Keyword(s):  
Diffusion Processes ◽  
First Passage Time ◽  
Passage Time ◽  
Continuous Functions ◽  
Probability Density Functions ◽  
Density Functions ◽  
First Passage ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Natural Boundaries

In this paper we study a Volterra integral equation of the second kind, including two arbitrary continuous functions, in order to determine first-passage-time probability density functions through time-dependent boundaries for time-non-homogeneous one-dimensional diffusion processes with natural boundaries. These results generalize those which were obtained for time-homogeneous diffusion processes by Giorno et al. [3], and for some particular classes of time-non-homogeneous diffusion processes by Gutiérrez et al. [4], [5].

A note on first passage times in birth and death and nonnegative diffusion processes

1983 ◽  
Vol 30 (2) ◽  
pp. 283-285 ◽  
Author(s):  
Cyrus Derman ◽  
Sheldon M. Ross ◽  
Zvi Schechner
Keyword(s):  
Diffusion Processes ◽  
First Passage Times ◽  
First Passage ◽  
Passage Times

A symmetry-based constructive approach to probability densities for one-dimensional diffusion processes

1989 ◽  
Vol 26 (4) ◽  
pp. 707-721 ◽  
Author(s):  
V. Giorno ◽  
A. G. Nobile ◽  
L. M. Ricciardi
Keyword(s):  
Diffusion Processes ◽  
First Passage Time ◽  
Passage Time ◽  
Constructive Approach ◽  
First Passage ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Probability Densities ◽  
Reflecting Boundaries ◽  
Natural Boundaries

Special symmetry conditions on the transition p.d.f. of one-dimensional time-homogeneous diffusion processes with natural boundaries are investigated and exploited to derive closed-form results concerning the transition p.d.f.'s in the presence of absorbing and reflecting boundaries and the first-passage-time p.d.f. through time-dependent boundaries.

An improved technique for the simulation of first passage times for diffusion processes

1999 ◽  
Vol 28 (4) ◽  
pp. 1135-1163 ◽  
Author(s):  
Maria Teresa Giraudo ◽  
Laura Sacerdote
Keyword(s):  
Diffusion Processes ◽  
First Passage Times ◽  
First Passage ◽  
Improved Technique ◽  
Passage Times

More general problems on first-passage times for diffusion processes: A new version of the fptdApprox R package

2014 ◽  
Vol 244 ◽  
pp. 432-446 ◽  
Author(s):  
P. Román-Román ◽  
J.J. Serrano-Pérez ◽  
F. Torres-Ruiz
Keyword(s):  
Diffusion Processes ◽  
R Package ◽  
First Passage Times ◽  
First Passage ◽  
Passage Times

On the asymptotic behaviour of first-passage-time densities for one-dimensional diffusion processes and varying boundaries

1990 ◽  
Vol 22 (4) ◽  
pp. 883-914 ◽  
Author(s):  
V. Giorno ◽  
A. G. Nobile ◽  
L. M. Ricciardi
Keyword(s):  
Asymptotic Behaviour ◽  
Diffusion Processes ◽  
First Passage Time ◽  
Sufficient Conditions ◽  
Passage Time ◽  
Asymptotic Results ◽  
First Passage ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Periodic Boundaries

Making use of the integral equations given in [1], [2] and [3], the asymptotic behaviour of the first-passage time (FPT) p.d.f.'s through certain time-varying boundaries, including periodic boundaries, is determined for a class of one-dimensional diffusion processes with steady-state density. Sufficient conditions are given for the cases both of single and of pairs of asymptotically constant and asymptotically periodic boundaries, under which the FPT densities asymptotically exhibit an exponential behaviour. Explicit expressions are then worked out for the processes that can be obtained from the Ornstein–Uhlenbeck process by spatial transformations. Some new asymptotic results for the FPT density of the Wiener process are finally proved, together with a few miscellaneous results.

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