Hitting probabilities of single points for processes with stationary independent increments by Harry Kesten

Cover of: Hitting probabilities of single points for processes with stationary independent increments | Harry Kesten

Published by American Mathematical Society in Providence .

Written in English

Read online

Subjects:

  • Probabilities.,
  • Markov processes.

Edition Notes

Book details

Statementby Harry Kesten.
SeriesMemoirs of the American Mathematical Society, no. 93, Memoirs of the American Mathematical Society -- no. 93.
The Physical Object
Pagination129 p.
Number of Pages129
ID Numbers
Open LibraryOL14119380M

Download Hitting probabilities of single points for processes with stationary independent increments

Get this from a library. Hitting probabilities of single points for processes with stationary independent increments.

[Harry Kesten] -- In this memoir the author considers a d-dimensional right-continuous process {[italic]X[italic subscript]t}[italic subscript]t≥0 with stationary independent increments. He seeks to determine when. Add tags for "Hitting probabilities of single points for processes with stationary independent increments".

Be the first. Genre/Form: Electronic books: Additional Physical Format: Print version: Kesten, Harry, Hitting probabilities of single points for processes with stationary independent increments /.

Hitting probabilities of single points for processes with stationary independent increments About this Title.

Harry Kesten. Publication: Memoirs of the American Mathematical SocietyCited by: Get this from a library. Hitting probabilities of single points for processes with stationary independed increments. [Harry Kesten]. Products of random matrices (with H. Furstenberg), Ann. Math. Statist.

31(), – Hitting Probabilities of Single Points for Processes with Stationary. abilities for scalar processes to hit points and small balls. We apply our results to the probabilities of hitting singletons and fractals in Rd, for a two-parameter class of processes.

This class is ne enough to narrow down where a phase transition to point polarity (zero probability of hitting singletons) might occur. Previously, the transition. Mamuro Kanda. Two theorems on capacity for Markov processes with stationary independent increments. Wahrscheinlichkeitstheorie verw.

Gebiete, pages Ж, Harry Kesten. Hitting Probabilities of Single Points for Processes with Stationary Independent Increments. Memoirs of the American Mathematical Society, No.

This paper is concerned with asymptotic behavior (at zero and at infinity) of the favorite points of Lévy processes. By exploring Molchan’s idea for deriving lower tail probabilities of Gaussian processes with stationary increments, we extend the result of Marcus (J Theor Probab 14(3)–, ) on the favorite points to a larger class of symmetric Lévy processes.

Cite this paper as: Meyer PA. () Démonstration probabiliste d'une identité de convolution. In: Séminaire Bourbaki vol. /69 Exposés Products of random matrices (with H.

Furstenberg), Ann. Math. Statist. 31 (), – Hitting Probabilities of Single Points for Processes with Stationary. [12] Kesten, H. Hitting probabilities of single points for processes with stationary independent increments. Memoirs of the American Mathematical Society, No.

93 American Mathematical Society, Providence, R.I. KESTEN H.-Hitting probabilities of single points for processes with stationary independent increments. (Mem. of A.M.S. n o 93, ). Google Scholar [10] MEYER P.A.-Probabilités et potentiels. Hermann-Paris. eBook Packages Springer Book Archive; Buy this book.

() Temps locaux d'intersection et points multiples des processus de levy. In: Azéma J., Yor M., Meyer P.A. (eds) Séminaire de Probabilités XXI. Lecture Notes in Mathematics, vol Part of the Lecture Notes in Mathematics book series (LNM, volume ) Abstract. Let (ξ, η Hitting probabilities of single points for processes with stationary independent increments.

Memoirs Amer. Math. Soc. Google Scholar. Klüppelberg, C., Lindner, A. and Maller, R. () A continuous time GARCH process driven by Lévy.

Hitting probabilities of single points for processes with stationary independent incre-ments Hitting probabilities of single points for processes with stationary independent increments. For one-dimensional symmetric L\'{e}vy processes, which hit every point with positive probability, we give sharp bounds for the tail function of the first hitting time of B which is either a.

Use extensively processes with special properties. Most notably, Gaussian pro-cesses are characterized entirely be means and covariances, Markov pro-cesses are characterized by one-step transition probabilities or transition rates, and initial distributions.

Independent increment processes are char-acterized by the distributions of single. Kesten, Harry. Hitting probabilities of single points for processes with stationary independent increments.

Memoirs of the American Mathematical Society, No. 93 American Mathematical Society, Providence, R.I. Le Jan, Yves. Markov paths, loops and fields. Lectures from the 38th Probability Summer School held in Saint-Flour, Selected Publications.

Products of random matrices (with H. Furstenberg), Ann. Math. Statist. 31 (), – Hitting Probabilities of Single Points for Processes with Stationary Independent Increments, Memoir no.

93, Amer. Math. Soc. Percolation Theory for Mathematicians, Birkhäuser, Boston, Aspects of first-passage percolation; in Ecole d'été de Probabilités de.

Sheldon M. Ross, in Introduction to Probability Models (Tenth Edition), Proposition T n, n = 1, 2,are independent identically distributed exponential random variables having mean 1 /λ.

Remark. The proposition should not surprise us. The assumption of stationary and independent increments is basically equivalent to asserting that, at any point in time, the process. Hitting probabilities for single points for processes of stationary independent increments (Memoirs of the AMS; 93).

AMS, Providence, R.I. como editor. Probability on discrete structures (Encyclopedia of mathematical sciences; ). Springer, BerlinISBN Hitting probabilities of single points for processes with stationary independent increments - Harry Kesten: MEMO/ Doubly timelike surfaces - John K.

Beem and Peter Y. Woo: MEMO/ An extension of Mackey’s method to Banach $*$-algebraic bundles - J. Fell: MEMO/ Formalized recursive functionals and formalized realizability. In probability, statistics and related fields, a Poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space.

The Poisson point process is often called simply the Poisson process, but it is also called a Poisson random measure, Poisson random point field or Poisson point point process has convenient mathematical. Hitting Probabilities Lecturer: James W. Pitman Scribe: Brian Milch Hitting probabilities Consider a Markov chain with a countable state space S and a transition matrix P.

Suppose we want to nd Pi(chain hits A before C) for some i 2 S and disjoint subsets A and C of S. We de ne the boundary B:= A[C. The remainder of this paper is devoted to study of processes X with independent increments, when Wiener's theory applies for prediction of R.E.

Feldman / Exit distributions 39 4. Prediction of Gaussian stationary processes We will need the following facts from the prediction theory of continuous-parameter stationary Gaussian processes.

Hitting probabilities in a Markov additive process with linear movements and upward jumps: Applications to risk and queueing processes Article (PDF Available) in The Annals of Applied Probability.

are jointly independent; the term stationary increments means that for any 0 process with stationary, independent increments is called a Levy´ process; more on these later.

The Wiener process is the intersection of the class. Comprised of 24 chapters, this book begins with an introduction to the second-order moments of a stationary Markov chain, paying particular attention to the consequences of the autoregressive structure of the vector-valued process and how to estimate the stationary probabilities from a.

a process is stationary if, in choosing any fixed point s as the origin, the ensuing process has the same probability law. An ergodic continuous-time Markov chain \(\{X(t),t\geq 0\}\) when \(\Pr[X(0)=j]=P_j,j\geq 0\), where \(P_j\) are the limiting probabilities.

a Markov chain whose initial state is chosen according to the limiting probabilities. hitting probabilities of single points for process with stationery independent increments jan 1, by Harry Kesten Paperback.

The process generated by the crossings of a fixed level, u, by the process Pn (t) is considered, where and the Xi (t) are identical, independent, separable, stationary, zero mean, Gaussian processes.

infinitesimal transition probabilities: P ij(h) = hq ij +o(h) for j 6= 0 P ii(h) = 1−hν i +o(h) • This can be used to simulate approximate sample paths by discretizing time into small intervals (the Euler method). • The Markov property is equivalent to independent increments for a Poisson counting process (which is a continuous Markov.

The time of hitting a single point x > 0 by the Wiener process is a random variable with the Lévy distribution. The family of these random variables (indexed by all positive numbers x) is a left-continuous modification of a Lévy process.

The right-continuous modification of this process is given by times of first exit from closed intervals [0. A new class of random composition structures (the ordered analog of Kingman’s partition structures) is defined by a regenerative description of component sizes. Each regenerative composition structure is represented by a process of random sampling of points from an exponential distribution on the positive halfline, and separating the points into clusters by an independent regenerative random.

The counting process {N(t), t ≥ 0} is said to be a Poisson process having rate λ, λ > 0 if it follows the following conditions: (1) N(0) = 0; (2) The process has independent increments; and (3) the number of events in any interval of length t is Poisson distributed with mean λt.

Don Kulasiri, Wynand Verwoerd, in North-Holland Series in Applied Mathematics and Mechanics, Introduction. In Chapter 2, we have introduced Brownian motion (the Wiener process) as a stationary, continuous stochastic process with independent process is a unique one to model the irregular noise such as Gaussian white noise in systems, and once such a process is.

The Airy process is stationary, it has continuous sample paths, its single “time” (fixed y) distribution is the Tracy–Widom distribution of the largest eigenvalue of a GUE random matrix, and. Along with the Bernoulli trials process and the Poisson process, the Brownian motion process is of central importance in of these processes is based on a set of idealized assumptions that lead to a rich mathematial theory.

In each case also, the process is used as a building block for a number of related random processes that are of great importance in a variety of applications. 2 1MarkovChains Introduction This section introduces Markov chains and describes a few examples. A discrete-time stochastic process {X n: n ≥ 0} on a countable set S is a collection of S-valued random variables defined on a probability space (Ω,F,P).The Pis a probability measure on a family of events F (a σ-field) in an event-space Ω.1 The set Sis the state space of the process, and the.

5 Winning at tennis What is your probability of winning a game of tennis, starting from the even score Deuce (), if your probability of winning each point is and your.(). Probabilities and Potential. North-Holland, Amsterdam. KESTEN, H. (). Hitting Probabilities of Single Points for Processes with Stationary Independent Increments.

Amer. TAy LOR, S. J. (). Sample path properties of processes with stationary independent increments. In Stochastic Analy sis (A Tribute to the Memory of Rollo.White noise is the simplest example of a stationary process. An example of a discrete-time stationary process where the sample space is also discrete (so that the random variable may take one of N possible values) is a Bernoulli examples of a discrete-time stationary process with continuous sample space include some autoregressive and moving average processes which are .

42641 views Wednesday, December 2, 2020