Cauchy Process Research Articles

Some Remarks on Asymmetric Processes

This paper contains three results: (a) an exact measure function for the zero set of a real-valued asymmetric Cauchy process, (b) an upper bound for the Hausdorff dimension of the zero set of a real process with stationary independent increments, and (c) an exact lower function at infinity for the completely asymmetric Cauchy process.

Measure function properties of the asymmetric Cauchy process

MathematikaVolume 17, Issue 1 p. 68-78 Research Article Measure function properties of the asymmetric Cauchy process John Hawkes, John Hawkes Department of Mathematics, University of Michigan, Ann Arbor, Michigan, U.S.A.Search for more papers by this author John Hawkes, John Hawkes Department of Mathematics, University of Michigan, Ann Arbor, Michigan, U.S.A.Search for more papers by this author First published: 01 June 1970 https://doi.org/10.1112/S0025579300002722Citations: 1AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume17, Issue1June 1970Pages 68-78 RelatedInformation

On a small drift of Cauchy process

On a small drift of Cauchy process

Spitzer's test for the cauchy process on the line

Spitzer's test for the cauchy process on the line

A two-sided absorption problem

Assuming as we may that the paths are right continuous, we denote by Tx the first passage time to the exterior of the open unit interval given that the process starts at x; TX = min{t: I X(t) ? I1. We shall obtain explicit formulas for the moments of T., and also for the distribution of the place of first passage X(T.). In the case of the symmetric Cauchy process these were obtained by Kac and Pollard [2] and Spitzer [4] respectively. 2. We set

On an ergodic property of a certain class of Markov processes

and (1.6) For fixed u, p(t, u) is a continuous function of t for t different from zero. The above conditions on the transition function are suggested by applications to the Brownian motion and, in the discrete case, to sums of independent random variables belonging to the domain of attraction of symmetric stable laws. There are Markov processes besides the Brownian motion for which conditions (1.1) to (1.6) are fulfilled, e.g. the Cauchy process with p(t, u) = t7r1l(t2 + u2)-. The main object of this paper is to prove an ergodic or equidistribution property of the Brownian motion process, a weak form of