Boundary Non-crossing Probabilities of Gaussian Processes: Sharp Bounds and Asymptotics

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Boundary Crossing Probabilities for Stationary Gaussian Processes and Brownian Motion1

Let X(t) be a stationary Gaussian process, /(/) a continuous function, and T a finite or infinite interval. This paper develops asymptotic estimates for P(X(t) > fit), some /er) when this probability is small. After transformation to an Ornstein Uhlenbeck process the results are also applicable to Brownian motion. In that special case, if W(t) is Brownian motion, / is continuously differentiabl...

متن کامل

On Boundary Crossing Probabilities for Diffusion Processes

In this paper we establish a relationship between the asymptotic form of conditional boundary crossing probabilities and first passage time densities for diffusion processes. We show that, under the assumption that the conditional probability that our diffusion (Xs, s ≥ 0) doesn’t cross an upper boundary g(·) prior to time t given that Xt = z behaves as (a+ o(1))(g(t)− z) as z ↑ g(t), there exi...

متن کامل

First Passage Densities and Boundary Crossing Probabilities for Diffusion Processes

We consider the boundary crossing problem for time-homogeneous diffusions and general curvilinear boundaries. Bounds are derived for the approximation error of the one-sided (upper) boundary crossing probability when replacing the original boundary by a different one. In doing so we establish the existence of the firstpassage time density and provide an upper bound for this function. In the cas...

متن کامل

Exact L2-small ball asymptotics of Gaussian processes and the spectrum of boundary value problems with ”non-separated” boundary conditions

We sharpen a classical result on the spectral asymptotics of the boundary value problems for self-adjoint ordinary differential operator. Using this result we obtain the exact L2-small ball asymptotics for a new class of zero mean Gaussian processes. This class includes, in particular, integrated generalized Slepian process, integrated centered Wiener process and integrated centered Brownian br...

متن کامل

SHARP ASYMPTOTICS OF THE FUNCTIONAL QUANTIZATION PROBLEM FOR GAUSSIAN PROCESSES By Harald Luschgy and Gilles Pagès

The sharp asymptotics for the L 2-quantization errors of Gaus-sian measures on a Hilbert space and, in particular, for Gaussian processes is derived. The condition imposed is regular variation of the eigenvalues. 1. Introduction. The quantization of probability distributions is an old story which starts in the late 1940s. It has been conceived in order to drastically cut down the storage of sig...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of Theoretical Probability

سال: 2020

ISSN: 0894-9840,1572-9230

DOI: 10.1007/s10959-020-01002-3