Level crossing probabilities for a multi-parameter Brownian process
نویسندگان
چکیده
منابع مشابه
On Approximation Rates for Boundary Crossing Probabilities for the Multivariate Brownian Motion Process
Motivated by an approximation problem from mathematical finance, we analyse the stability of the boundary crossing probability for the multivariate Brownian motion process, with respect to small changes of the boundary. Under broad assumptions on the nature of the boundary, including the Lipschitz condition (in a Hausdorff-type metric) on its time cross-sections, we obtain an analogue of the Bo...
متن کاملAnalytic crossing probabilities for certain barriers by Brownian motion
We calculate crossing probabilities and one-sided last exit time densities for a class of moving barriers on an interval [0, T ] via Schwartz distributions. We derive crossing probabilities and first hitting time densities for another class of barriers on [0, T ] by proving a Schwartz distribution version of the method of images. Analytic expressions for crossing probabilities and related densi...
متن کاملBoundary 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 کاملApproximate Level-crossing Probabilities for Interactive Visualization of Uncertain Isocontours
A major method for quantitative visualization of a scalar field is depiction of its isocontours. If the scalar field is afflicted with uncertainties, uncertain counterparts to isocontours have to be extracted and depicted. We consider the case where the input data is modeled as a discretized Gaussian field with spatial correlations. For this situation we want to compute level-crossing probabili...
متن کاملAvoiding-probabilities for Brownian Snakes and Super-brownian Motion Avoiding-probabilities for Brownian Snakes and Super-brownian Motion
We investigate the asymptotic behaviour of the probability that a normalized d-dimensional Brownian snake (for instance when the lifetime process is an excursion of height 1) avoids 0 when starting at distance " from the origin. In particular we show that when " tends to 0, this probability respectively behaves (up to multiplicative constants) like " 4 , " 2 p 2 and " (p 17?1)=2 , when d = 1, d...
متن کاملذخیره 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: Pacific Journal of Mathematics
سال: 1976
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1976.65.223