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Strongly Elliptic Systems and Boundary Integral Equations
, 2000
"... Partial differential equations provide mathematical models of many important problems in the physical sciences and engineering. This book treats one class of such equations, concentrating on methods involving the use of surface potentials. It provides the first detailed exposition of the mathematic ..."
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Cited by 501 (0 self)
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Partial differential equations provide mathematical models of many important problems in the physical sciences and engineering. This book treats one class of such equations, concentrating on methods involving the use of surface potentials. It provides the first detailed exposition
The WienerAskey Polynomial Chaos for Stochastic Differential Equations
 SIAM J. SCI. COMPUT
, 2002
"... We present a new method for solving stochastic differential equations based on Galerkin projections and extensions of Wiener's polynomial chaos. Specifically, we represent the stochastic processes with an optimum trial basis from the Askey family of orthogonal polynomials that reduces the dime ..."
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Cited by 398 (42 self)
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We present a new method for solving stochastic differential equations based on Galerkin projections and extensions of Wiener's polynomial chaos. Specifically, we represent the stochastic processes with an optimum trial basis from the Askey family of orthogonal polynomials that reduces
New results in linear filtering and prediction theory
 TRANS. ASME, SER. D, J. BASIC ENG
, 1961
"... A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary sta ..."
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Cited by 607 (0 self)
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A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary
Modeling and simulation of genetic regulatory systems: A literature review
 JOURNAL OF COMPUTATIONAL BIOLOGY
, 2002
"... In order to understand the functioning of organisms on the molecular level, we need to know which genes are expressed, when and where in the organism, and to which extent. The regulation of gene expression is achieved through genetic regulatory systems structured by networks of interactions between ..."
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Cited by 738 (14 self)
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, ordinary and partial differential equations, qualitative differential equations, stochastic equations, and rulebased formalisms. In addition, the paper discusses how these formalisms have been used in the simulation of the behavior of actual regulatory systems.
An equilibrium characterization of the term structure.
 J. Financial Econometrics
, 1977
"... The paper derives a general form of the term structure of interest rates. The following assumptions are made: (A.l) The instantaneous (spot) interest rate follows a diffusion process; (A.2) the price of a discount bond depends only on the spot rate over its term; and (A.3) the market is efficient. ..."
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Cited by 1041 (0 self)
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. Under these assumptions, it is shown by means of an arbitrage argument that the expected rate of return on any bond in excess of the spot rate is proportional to its standard deviation. This property is then used to derive a partial differential equation for bond prices. The solution to that equation
Loopy belief propagation for approximate inference: An empirical study. In:
 Proceedings of Uncertainty in AI,
, 1999
"... Abstract Recently, researchers have demonstrated that "loopy belief propagation" the use of Pearl's polytree algorithm in a Bayesian network with loops can perform well in the context of errorcorrecting codes. The most dramatic instance of this is the near Shannonlimit performanc ..."
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Cited by 676 (15 self)
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. That is, we replaced the reference to >.� ) in and similarly for 11"�) in Equation 3, where 0 :::; J.l :::; 1 is the momentum term. It is easy to show that if the modified system of equations converges to a fixed point F, then F is also a fixed point of the original system (since if>.� ) = >
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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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
Testing ContinuousTime Models of the Spot Interest Rate
 Review of Financial Studies
, 1996
"... Different continuoustime models for interest rates coexist in the literature. We test parametric models by comparing their implied parametric density to the same density estimated nonparametrically. We do not replace the continuoustime model by discrete approximations, even though the data are rec ..."
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Cited by 310 (9 self)
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to specify an appropriate stochastic differential equation is for the most part an unanswered question. For example, many different continuoustime The comments and suggestions of Kerry Back (the editor) and an anonymous referee were very helpful. I am also grateful to George Constantinides,
Pricing with a Smile
 Risk Magazine
, 1994
"... prices as a function of volatility. If an option price is given by the market we can invert this relationship to get the implied volatility. If the model were perfect, this implied value would be the same for all option market prices, but reality shows this is not the case. Implied Black–Scholes vol ..."
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Cited by 445 (1 self)
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the former is the quadratic mean of the latter. The spot process S is then governed by the following stochastic differential equation: dS �rt () dt��() t dW
A Fluidbased Analysis of a Network of AQM Routers Supporting TCP Flows with an Application to RED
 Proc. SIGCOMM 2000
, 2000
"... In this paper we use jump process driven Stochastic Differential Equations to model the interactions of a set of TCP flows and Active Queue Management routers in a network setting. We show how the SDEs can be transformed into a set of Ordinary Differential Equations which can be easily solved numeri ..."
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Cited by 417 (21 self)
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In this paper we use jump process driven Stochastic Differential Equations to model the interactions of a set of TCP flows and Active Queue Management routers in a network setting. We show how the SDEs can be transformed into a set of Ordinary Differential Equations which can be easily solved
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