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A class of integration by parts formulae in stochastic analysis I
"... Introduction Consider a Stratonovich stochastic differential equation dx t = X(x t ) ffi dB t +A(x t )dt (1) with C 1 coefficients on a compact Riemannian manifold M , with associated differential generator A = 1 2 \Delta M +Z and solution flow f¸ t : t 0g of random smooth diffeomorphisms of ..."
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Cited by 19 (10 self)
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Introduction Consider a Stratonovich stochastic differential equation dx t = X(x t ) ffi dB t +A(x t )dt (1) with C 1 coefficients on a compact Riemannian manifold M , with associated differential generator A = 1 2 \Delta M +Z and solution flow f¸ t : t 0g of random smooth diffeomorphisms
Differentiation of Heat Semigroups and Applications
, 1994
"... Introduction Consider the Stratonovich stochastic differential equation dx t = X(x t ) ffi dB t +A(x t )dt: (1) on R n with coefficients A : R n ! R n a smooth vector field and X : R n ! L (R m ; R n ) a smooth map into the space of linear maps of R m into R n , driven by the white ..."
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Introduction Consider the Stratonovich stochastic differential equation dx t = X(x t ) ffi dB t +A(x t )dt: (1) on R n with coefficients A : R n ! R n a smooth vector field and X : R n ! L (R m ; R n ) a smooth map into the space of linear maps of R m into R n , driven
Concerning the Geometry of Stochastic Differential Equations and Stochastic Flows
 Kusuoka and I. Shigekawa (Eds.) New Trends in Stochastic Analysis. Proc. Taniguchi Symposium
, 1995
"... Le Jan and Watanabe showed that a nondegenerate stochastic flow f¸ t : t 0g on a manifold M determines a connection on M . This connection is characterized here and shown to be the LeviCivita connection for gradient systems. This both explains why such systems have useful properties and allows u ..."
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Cited by 16 (10 self)
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Bochner vanishing theorem. 1 Introduction and Notations A. Consider a Stratonovich stochastic differential equation dx t = X(x t ) ffi dB t +A(x t )dt (1) on an ndimensional C 1 manifold M , e.g. M = R n . Here A is a C 1 vector field on M , so A(x) lies in the tangent space T x M to M at x
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.
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
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
Grounding in communication
 In
, 1991
"... We give a general analysis of a class of pairs of positive selfadjoint operators A and B for which A + XB has a limit (in strong resolvent sense) as h10 which is an operator A, # A! Recently, Klauder [4] has discussed the following example: Let A be the operator(d2/A2) + x2 on L2(R, dx) and let ..."
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Cited by 1122 (20 self)
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B = 1 x 1s. The eigenvectors and eigenvalues of A are, of course, well known to be the Hermite functions, H,(x), n = 0, l,... and E, = 2n + 1. Klauder then considers the eigenvectors of A + XB (A> 0) by manipulations with the ordinary differential equation (we consider the domain questions
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
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
Results 1  10
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