Results 11  20
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8,259
Efficient exact stochastic simulation of chemical systems with many species and many channels
 J. Phys. Chem. A
, 2000
"... There are two fundamental ways to view coupled systems of chemical equations: as continuous, represented by differential equations whose variables are concentrations, or as discrete, represented by stochastic processes whose variables are numbers of molecules. Although the former is by far more comm ..."
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Cited by 427 (5 self)
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chemical reactions that is also efficient: it (a) uses only a single random number per simulation event, and (b) takes time proportional to the logarithm of the number of reactions, not to the number of reactions itself. The Next Reaction Method is extended to include timedependent rate constants and nonMarkov
A Markov Model for the Term Structure of Credit Risk Spreads
 Review of Financial Studies
, 1997
"... This article provides a Markov model for the term structure of credit risk spreads. The model is based on Jarrow and Turnbull (1995), with the bankruptcy process following a discrete state space Markov chain in credit ratings. The parameters of this process are easily estimated using observable data ..."
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Cited by 377 (12 self)
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This article provides a Markov model for the term structure of credit risk spreads. The model is based on Jarrow and Turnbull (1995), with the bankruptcy process following a discrete state space Markov chain in credit ratings. The parameters of this process are easily estimated using observable
A Logic for Reasoning about Time and Reliability
 Formal Aspects of Computing
, 1994
"... We present a logic for stating properties such as, "after a request for service there is at least a 98% probability that the service will be carried out within 2 seconds". The logic extends the temporal logic CTL by Emerson, Clarke and Sistla with time and probabilities. Formulas are inter ..."
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Cited by 371 (1 self)
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are interpreted over discrete time Markov chains. We give algorithms for checking that a given Markov chain satisfies a formula in the logic. The algorithms require a polynomial number of arithmetic operations, in size of both the formula and This research report is a revised and extended version of a paper
with Nonhomogeneous Markov Chains
"... Modelling structural coverage and the number of failure occurrences with nonhomogeneous Markov chains ..."
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Modelling structural coverage and the number of failure occurrences with nonhomogeneous Markov chains
Numerical Solution of NonHomogeneous Markov Processes through Uniformization
"... Numerical algorithms based on uniformization have been proven to be numerically stable and computationally attractive to compute transient state distributions in homogeneous continuoustime Markov chains. Recently, Van Dijk [van Dijk, 1992] formulated uniformization for non homogeneous Markov proce ..."
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Cited by 12 (0 self)
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Numerical algorithms based on uniformization have been proven to be numerically stable and computationally attractive to compute transient state distributions in homogeneous continuoustime Markov chains. Recently, Van Dijk [van Dijk, 1992] formulated uniformization for non homogeneous Markov
Approximate counting, uniform generation and rapidly mixing markov chains
 Inf. Comput
, 1989
"... The paper studies effective approximate solutions to combinatorial counting and uniform generation problems. Using a technique based on the simulation of ergodic Markov chains, it is shown that, for selfreducible structures, almost uniform generation is possible in polynomial time provided only tha ..."
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Cited by 317 (11 self)
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The paper studies effective approximate solutions to combinatorial counting and uniform generation problems. Using a technique based on the simulation of ergodic Markov chains, it is shown that, for selfreducible structures, almost uniform generation is possible in polynomial time provided only
Verifying Continuous Time Markov Chains
, 1996
"... . We present a logical formalism for expressing properties of continuous time Markov chains. The semantics for such properties arise as a natural extension of previous work on discrete time Markov chains to continuous time. The major result is that the verification problem is decidable; this is show ..."
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Cited by 125 (1 self)
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. We present a logical formalism for expressing properties of continuous time Markov chains. The semantics for such properties arise as a natural extension of previous work on discrete time Markov chains to continuous time. The major result is that the verification problem is decidable
Hidden Markov processes
 IEEE Trans. Inform. Theory
, 2002
"... Abstractâ€”An overview of statistical and informationtheoretic aspects of hidden Markov processes (HMPs) is presented. An HMP is a discretetime finitestate homogeneous Markov chain observed through a discretetime memoryless invariant channel. In recent years, the work of Baum and Petrie on finite ..."
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Cited by 264 (5 self)
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Abstractâ€”An overview of statistical and informationtheoretic aspects of hidden Markov processes (HMPs) is presented. An HMP is a discretetime finitestate homogeneous Markov chain observed through a discretetime memoryless invariant channel. In recent years, the work of Baum and Petrie on finite
The twoparameter PoissonDirichlet distribution derived from a stable subordinator.
, 1995
"... The twoparameter PoissonDirichlet distribution, denoted pd(ff; `), is a distribution on the set of decreasing positive sequences with sum 1. The usual PoissonDirichlet distribution with a single parameter `, introduced by Kingman, is pd(0; `). Known properties of pd(0; `), including the Markov ..."
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Cited by 356 (33 self)
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of Brownian motion and Bessel processes. For 0 ! ff ! 1, pd(ff; 0) is the asymptotic distribution of ranked lengths of excursions of a Markov chain away from a state whose recurrence time distribution is in the domain of attraction of a stable law of index ff. Formulae in this case trace back to work
Multicommodity maxflow mincut theorems and their use in designing approximation algorithms
 J. ACM
, 1999
"... In this paper, we establish maxflow mincut theorems for several important classes of multicommodity flow problems. In particular, we show that for any nnode multicommodity flow problem with uniform demands, the maxflow for the problem is within an O(log n) factor of the upper bound implied by ..."
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Cited by 357 (6 self)
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, network reconfiguration, communication in distributed networks, scientific computing and rapidly mixing Markov chains are also described in the paper.
Results 11  20
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8,259