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An introduction to probability theory and its applications

01 Jan 1950-

About: The article was published on 1950-01-01 and is currently open access. It has received 31510 citation(s) till now. The article focuses on the topic(s): Probability and statistics & Imprecise probability.
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Book
01 Jan 1996-
TL;DR: A valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography, this book provides easy and rapid access of information and includes more than 200 algorithms and protocols.
Abstract: From the Publisher: A valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography, this book provides easy and rapid access of information and includes more than 200 algorithms and protocols; more than 200 tables and figures; more than 1,000 numbered definitions, facts, examples, notes, and remarks; and over 1,250 significant references, including brief comments on each paper.

13,370 citations


Book ChapterDOI
Wassily Hoeffding1Institutions (1)
Abstract: Upper bounds are derived for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt. It is assumed that the range of each summand of S is bounded or bounded above. The bounds for Pr {S – ES ≥ nt} depend only on the endpoints of the ranges of the summands and the mean, or the mean and the variance of S. These results are then used to obtain analogous inequalities for certain sums of dependent random variables such as U statistics and the sum of a random sample without replacement from a finite population.

8,475 citations


Journal ArticleDOI
Steven L. Heston1Institutions (1)
Abstract: I use a new technique to derive a closed-form solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and spotasset returns. I introduce stochastic interest rates and show how to apply the model to bond options and foreign currency options. Simulations show that correlation between volatility and the spot asset’s price is important for explaining return skewness and strike-price biases in the BlackScholes (1973) model. The solution technique is based on characteristi c functions and can be applied to other problems.

7,295 citations


01 Jul 2003-
TL;DR: RTP provides end-to-end network transport functions suitable for applications transmitting real-time data over multicast or unicast network services and is augmented by a control protocol (RTCP) to allow monitoring of the data delivery in a manner scalable to large multicast networks.
Abstract: This memorandum describes RTP, the real-time transport protocol. RTP provides end-to-end network transport functions suitable for applications transmitting real-time data, such as audio, video or simulation data, over multicast or unicast network services. RTP does not address resource reservation and does not guarantee quality-of-service for real-time services. The data transport is augmented by a control protocol (RTCP) to allow monitoring of the data delivery in a manner scalable to large multicast networks, and to provide minimal control and identification functionality. RTP and RTCP are designed to be independent of the underlying transport and network layers. The protocol supports the use of RTP-level translators and mixers.

7,115 citations


Journal ArticleDOI
Ralf Metzler1, Joseph Klafter1Institutions (1)
01 Dec 2000-Physics Reports
Abstract: Fractional kinetic equations of the diffusion, diffusion–advection, and Fokker–Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns. These fractional equations are derived asymptotically from basic random walk models, and from a generalised master equation. Several physical consequences are discussed which are relevant to dynamical processes in complex systems. Methods of solution are introduced and for some special cases exact solutions are calculated. This report demonstrates that fractional equations have come of age as a complementary tool in the description of anomalous transport processes.

6,586 citations


Network Information
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No. of citations received by the Paper in previous years
YearCitations
20229
2021550
2020649
2019640
2018612
2017686