A chain with complete connections Sample Clauses

A chain with complete connections. We construct a chain with complete connections that carries the necessary information relative to the evolution of the path of the RW Z in (2.29), together with the states of the RE ξ inside the truncated cones visited by the path between regeneration times. Lemma 3.3 below uses the n-cone-mixing property to control the dependence of the future evolution of the chain on its past. In particular, we will see that the influence of the past decays as fast as the correlations in the RE. We start by defining the relevant state space. Recall (3.1) and for N ∈ N let PN = x = (x(0), x(1), . . . , x(N )) ∈ CN (0)N : { } (3.7) be the set of possible paths of the process Z within the truncated cone CN (0), where x(i + 1) ∼ x(i) stands for |x1(i + 1) − x1(i)| = 1, x2(i + 1) − x2(i) = 1. Define ∪ T = {N} × PN × EN , (3.8) N∈N where EN = {ξt(z): (z, t) ∈ CN (0)} is the set of possible values of the environment ξ in the cone CN (0). Let W = {T ∪ {s}}N (3.9) be the set of infinite vectors with components either in T or equal to the stopping symbol s, with the restriction that if wk = s then wi = s for i ≥ k. Note that, for fixed k k∈N L ∈ N, the sequence of regeneration times (τ (L)) in (2.35), together with the path Z, determine an infinite sequence r = (r1, r2, . . . ) ∈ W given by τk )}) rk = (S k+1,L , Z ( (L) τk +j Sk+1,L ) {, ξ (z): (z, t) ∈ C t j=1 Sk+1,L (Z (L) ∈ T , k ∈ N, (3.10) with Sk,L = τ (L) − τ (L) − L, k ∈ N. (3.11) k k−1 1
Sample 1
AutoNDA by SimpleDocs

Related to A chain with complete connections

  • Notices Any notice, request or other document required or permitted to be given or delivered to the Holder by the Company shall be delivered in accordance with the notice provisions of the Purchase Agreement.

  • IN WITNESS WHEREOF the parties hereto have executed this Agreement as of the day and year first above written.

  • Entire Agreement This Agreement constitutes the entire agreement between the parties hereto with respect to the subject matter contained in this Agreement and supersedes all prior agreements, understandings and negotiations between the parties.

  • Insurance The Company and the Subsidiaries are insured by insurers of recognized financial responsibility against such losses and risks and in such amounts as are prudent and customary in the businesses in which the Company and the Subsidiaries are engaged, including, but not limited to, directors and officers insurance coverage. Neither the Company nor any Subsidiary has any reason to believe that it will not be able to renew its existing insurance coverage as and when such coverage expires or to obtain similar coverage from similar insurers as may be necessary to continue its business without a significant increase in cost.

  • WHEREAS the Company desires the Warrant Agent to act on behalf of the Company, and the Warrant Agent is willing to so act, in connection with the issuance, registration, transfer, exchange, redemption and exercise of the Warrants; and

  • Termination This Agreement may be terminated at any time prior to the Closing:

  • Severability Any provision of this Agreement that is prohibited or unenforceable in any jurisdiction shall, as to such jurisdiction, be ineffective to the extent of such prohibition or unenforceability without invalidating the remaining provisions hereof, and any such prohibition or unenforceability in any jurisdiction shall not invalidate or render unenforceable such provision in any other jurisdiction.

  • NOW, THEREFORE the parties hereto agree as follows:

  • Definitions For purposes of this Agreement:

  • General All payments to be made by the Borrower shall be made without condition or deduction for any counterclaim, defense, recoupment or setoff. Except as otherwise expressly provided herein, all payments by the Borrower hereunder shall be made to the Administrative Agent, for the account of the respective Lenders to which such payment is owed, at the Administrative Agent’s Office in Dollars and in immediately available funds not later than 2:00 p.m. on the date specified herein. The Administrative Agent will promptly distribute to each Lender its Applicable Percentage (or other applicable share as provided herein) of such payment in like funds as received by wire transfer to such Lender’s Lending Office. All payments received by the Administrative Agent after 2:00 p.m. shall be deemed received on the next succeeding Business Day and any applicable interest or fee shall continue to accrue. If any payment to be made by the Borrower shall come due on a day other than a Business Day, payment shall be made on the next following Business Day, and such extension of time shall be reflected in computing interest or fees, as the case may be.

Draft better contracts in just 5 minutes Get the weekly Law Insider newsletter packed with expert videos, webinars, ebooks, and more!