Journal ArticleDOI
Solving an Inverse First-Passage-Time Problem for Wiener Process Subject to Random Jumps from a Boundary
TLDR
In this article, an inverse first-passage-time problem for Wiener process X(t) subject to random jumps from a boundary c is studied, where the problem consists of finding the distribution of the jumps which occur when X( t) hits c, so that the first passage time of X (t) through S has distribution F.Abstract:
We study an inverse first-passage-time problem for Wiener process X(t) subject to random jumps from a boundary c. Let be given a threshold S > X(0); and a distribution function F on [0, + ∞). The problem consists of finding the distribution of the jumps which occur when X(t) hits c, so that the first-passage time of X(t) through S has distribution F.read more
Citations
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Book ChapterDOI
Stochastic Differential Equations
TL;DR: In this paper, the authors explore questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties, using diffusion processes as a model of a Markov process with continuous sample paths.
Journal ArticleDOI
Estimating a non-homogeneous Gompertz process with jumps as model of tumor dynamics
TL;DR: A non-homogeneous stochastic model based on a Gompertz-type diffusion process with jumps is proposed to describe the evolution of a solid tumor subject to an intermittent therapeutic program that instantly reduces the tumor size to a fixed value and increases the growth rate of the model to represent the toxicity of the therapy.
Journal ArticleDOI
On the excursions of drifted Brownian motion and the successive passage times of Brownian motion
TL;DR: In this paper, the distribution of the n th passage time of Brownian motion through a straight line S ( t ) = a + b t for the special case when b = 0 was studied.
Journal ArticleDOI
Diffusion Processes and Related Topics in Biology.
TL;DR: In this article, the authors introduce diffusion models for Neuronal Activity in a random environment and compare them to the Feller Process and the Schrodinger Equation of the first passage time problem.
References
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Book ChapterDOI
Stochastic Differential Equations
TL;DR: In this paper, the authors explore questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties, using diffusion processes as a model of a Markov process with continuous sample paths.
Book
Stochastic differential equations
TL;DR: In this article, the authors introduce the notion of a stochastic differential equation and prove general theorems concerning the existence and uniqueness of solutions of these equations, which is a generalization of the notions of integral integral integral functions.
Journal ArticleDOI
The first passage problem for a continuous markoff process
D. A. Darling,A. J. F. Siegert +1 more
TL;DR: In this paper, the first passage problem for a strongly continuous temporally homogeneous Markoff process X(t) is given, where T = T sub ab (x) is a random variable giving the time of first passage of X (t) b when a X(0) = x b, and simple methods of getting the distribution of T (at least in terms of a Laplace transform) are developed.