Results 1  10
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751
Parameter estimation for Ornstein–Uhlenbeck processes driven by αstable Lévy motions
 Long / Stochastic Processes and their Applications 119
, 2007
"... Abstract. The parameter estimation theory for stochastic dierential equations driven by Brownian motions or general Levy processes with nite second moments has been well developed. In this paper, we consider the parameter estimation problem for OrnsteinUhlenbeck processes driven by stable Levy mo ..."
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Cited by 11 (2 self)
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Abstract. The parameter estimation theory for stochastic dierential equations driven by Brownian motions or general Levy processes with nite second moments has been well developed. In this paper, we consider the parameter estimation problem for OrnsteinUhlenbeck processes driven by stable Levy
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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tiply connected networks: When loops are present, the network is no longer singly connected and local propaga tion schemes will invariably run into trouble . We believe there are general undiscovered theorems about the performance of belief propagation on loopy DAGs. These theo rems, which may have
Hellenic Capital Market Commission
, 1998
"... Jumping diusion models for nancial prices and returns are nding increasing application in the pricing of current contingent claims. Generalizing the theory for a Markov process with continuous sample paths { characterized in terms of its innitesimal generator { we establish existence and uniqueness ..."
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and uniqueness of solutions to jump stochastic dierential equations. We adapt the Stroock and Varadhan approach, which develops a variant of the `weak sense ' solution of a stochastic dierential equation by formulating it as a diusion process solution of a martingale problem. Our approach to deriving
Numerical solution of secondorder stochastic dierential equations with Gaussian random parameters
, 2013
"... Abstract. In this paper, we present the numerical solution of ordinary dierential equations (or SDEs), from each order especially secondorder with timevarying and Gaussian random coecients. We indicate a complete analysis for secondorder equations in special case of scalar linear secondorder equ ..."
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fundamental matrix of this system, it could be calculated based on the exact solution of this system. Finally, this stochastic equation is solved by numerically method like EulerMaruyama and Milstein. Also its Asymptotic stability and statistical concepts like expectation and variance of solutions
Jacobianfree NewtonKrylov methods: a survey of approaches and applications
 J. Comput. Phys
"... Jacobianfree NewtonKrylov (JFNK) methods are synergistic combinations of Newtontype methods for superlinearly convergent solution of nonlinear equations and Krylov subspace methods for solving the Newton correction equations. The link between the two methods is the Jacobianvector product, which ..."
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Cited by 204 (6 self)
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Jacobianfree NewtonKrylov (JFNK) methods are synergistic combinations of Newtontype methods for superlinearly convergent solution of nonlinear equations and Krylov subspace methods for solving the Newton correction equations. The link between the two methods is the Jacobianvector product
On the stochastic aubrymather theory
, 2004
"... Abstract. In this paper we prove the dierentiability of the stochastic analogues of Mather's functions and , introduced implicitly by D. Gomes [G]. We also prove that the solution to the viscous Hamilton Jacobi equation associated to is dierentiable in the parameter. 1. ..."
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Cited by 3 (0 self)
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Abstract. In this paper we prove the dierentiability of the stochastic analogues of Mather's functions and , introduced implicitly by D. Gomes [G]. We also prove that the solution to the viscous Hamilton Jacobi equation associated to is dierentiable in the parameter. 1.
HighOrder Collocation Methods for Differential Equations with Random Inputs
 SIAM Journal on Scientific Computing
"... Abstract. Recently there has been a growing interest in designing efficient methods for the solution of ordinary/partial differential equations with random inputs. To this end, stochastic Galerkin methods appear to be superior to other nonsampling methods and, in many cases, to several sampling met ..."
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Cited by 188 (13 self)
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methods. However, when the governing equations take complicated forms, numerical implementations of stochastic Galerkin methods can become nontrivial and care is needed to design robust and efficient solvers for the resulting equations. On the other hand, the traditional sampling methods, e.g., Monte
On Weak Convergence, Malliavin Calculus and Kolmogorov Equa tions in Infinite Dimensions
"... This thesis is focused around weak convergence analysis of approximations of stochastic evolution equations in Hilbert space. This is a class of problems, which is sufficiently challenging to motivate new theoretical developments in stochastic analysis. The first paper of the thesis further develo ..."
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This thesis is focused around weak convergence analysis of approximations of stochastic evolution equations in Hilbert space. This is a class of problems, which is sufficiently challenging to motivate new theoretical developments in stochastic analysis. The first paper of the thesis further
ELECTRONIC COMMUNICATIONS in PROBABILITY OSCILLATION AND NON{OSCILLATION IN SOLU TIONS OF NONLINEAR STOCHASTIC DELAY DIF FERENTIAL EQUATIONS
, 2004
"... This paper studies the oscillation and nonoscillation of solutions of a nonlinear stochastic delay di®erential equation, where the noise perturbation depends on the current state, and the drift depends on a delayed argument. When the restoring force towards equilibrium is relatively strong, all solu ..."
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This paper studies the oscillation and nonoscillation of solutions of a nonlinear stochastic delay di®erential equation, where the noise perturbation depends on the current state, and the drift depends on a delayed argument. When the restoring force towards equilibrium is relatively strong, all
Extending Martingale Measure Stochastic Integral With Applications To Spatially Homogeneous S.p.d.e's
 S.P.D.E.'S, Electronic Journal of Probability 4, 129, http://www.math.washington.edu/ ejpecp/EjpVol4/paper6.abs.html
, 1999
"... We extend the definition of Walsh's martingale measure stochastic integral so as to be able to solve stochastic partial di#erential equations whose Green's function is not a function but a Schwartz distribution. This is the case for the wave equation in dimensions greater than two. Even wh ..."
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Cited by 140 (11 self)
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We extend the definition of Walsh's martingale measure stochastic integral so as to be able to solve stochastic partial di#erential equations whose Green's function is not a function but a Schwartz distribution. This is the case for the wave equation in dimensions greater than two. Even
Results 1  10
of
751