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[PDF] Top 20 Path Integral Methods for Stochastic Differential Equations

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Path Integral Methods for Stochastic Differential Equations

Path Integral Methods for Stochastic Differential Equations

... the integral will be dominated by the critical points of the exponent of the ...“classical” equations of motion (mean field theory in statistical ...and stochastic analysis this is also known as a ... See full document

35

Stability of stochastic differential equations in infinite dimensions

Stability of stochastic differential equations in infinite dimensions

... functional differential equations such as differential equations with memory, even with constant delays, since the history of the process must be taken into ...general methods such as ... See full document

203

Accurate stationary densities with partitioned numerical methods for stochastic partial differential equations

Accurate stationary densities with partitioned numerical methods for stochastic partial differential equations

... of stochastic systems that are second order in time depends on the damping parameter, η ...order stochastic differential equations with additive noise and a damping term, it is possible to ... See full document

15

Adaptive Methods Exploring Intrinsic Sparse Structures of Stochastic Partial Differential Equations

Adaptive Methods Exploring Intrinsic Sparse Structures of Stochastic Partial Differential Equations

... numerical methods for SPDEs, such as MC, qMC, gPC, and gSC, additional post-processing steps are necessary to get the KL expansions of stochastic ...DyBO methods explore the inherent low-dimensional ... See full document

224

Numerical solution of higher index DAEs using their IAE's structure: Trajectory-prescribed path control problem and simple pendulum

Numerical solution of higher index DAEs using their IAE's structure: Trajectory-prescribed path control problem and simple pendulum

... collocation methods on the piecewise polynomials spaces are very suitable for the equations with integral or differential ...operator equations, their convergence orders don’t change when the ... See full document

15

New S-ROCK methods for stochastic differential equations with commutative noise

New S-ROCK methods for stochastic differential equations with commutative noise

... < 1 } . (18) For more clear results concerning the MS-stability regions of SROCKC2 schemes, in the following, we confine our investigation to some optimal values of η and s, which have been suggested by [14]. The ... See full document

23

Error estimates of finite element methods for nonlinear fractional stochastic differential equations

Error estimates of finite element methods for nonlinear fractional stochastic differential equations

... In this paper, we consider the Galerkin finite element approximations of the initial value problem for the nonlinear fractional stochastic partial differential equations with multiplicative noise. We study a ... See full document

20

Exact Solution of Fractional Black Scholes European Option Pricing Equations

Exact Solution of Fractional Black Scholes European Option Pricing Equations

... numerical methods, the VIM and the ADM are the most popu- lar ones that are used to solve differential and integral equations of integer and fractional ...ordinary differential ... See full document

15

Stability for a class of semilinear fractional stochastic integral equations

Stability for a class of semilinear fractional stochastic integral equations

... numerical methods for fractional partial differential equations [–], among ...of stochastic fractional differential equations using different ... See full document

20

Stochastic Runge-Kutta method for stochastic delay differential equations

Stochastic Runge-Kutta method for stochastic delay differential equations

... This study was undertaken to generalize the convergence proof of numerical methods for SDDEs when the drift and diffusion are Taylor expansion as well as to propose a derivative–free method, i.e. SRK up to order ... See full document

30

Multi level Monte Carlo methods for the approximation of invariant measures of stochastic differential equations

Multi level Monte Carlo methods for the approximation of invariant measures of stochastic differential equations

... introduced stochastic gradient Langevin dynamics method (Welling and Teh, in: Proceedings of the 28th ICML, 2011) built for large datasets ...first stochastic gradient MCMC method with complexity O(ε − 2 | ... See full document

18

Stochastic differential equations and integrating factor

Stochastic differential equations and integrating factor

... of stochastic processes with respect to stochastic ...best-known stochastic process to which stochastic calculus is applied the Wiener ... See full document

6

Quasilinear Stochastic Partial Differential Equations

Quasilinear Stochastic Partial Differential Equations

... Suppose we have a measure space (M, A, µ) and a Banach space X. We may assume X is a separable Banach space, since in our applications, the function spaces we look at are separable. This will simplify matters when ... See full document

88

Multiscale Model Reduction Methods for Deterministic and Stochastic Partial Differential Equations

Multiscale Model Reduction Methods for Deterministic and Stochastic Partial Differential Equations

... Model reduction technique for PDEs. We have proposed a multiscale model reduction method for several standard types of elliptic, parabolic, hyperbolic, and convection-diffusion equations. A key ingredient of this ... See full document

118

Path-Integral Methods for Analyzing the Effects of Fluctuations in Stochastic Hybrid Neural Networks

Path-Integral Methods for Analyzing the Effects of Fluctuations in Stochastic Hybrid Neural Networks

... One of the major challenges in neuroscience is developing our understanding of how noise at the molecular and cellular levels affects dynamics and information process- ing at the macroscopic level of synaptically coupled ... See full document

33

Structure preserving stochastic Runge–Kutta–Nyström methods for nonlinear second order stochastic differential equations with multiplicative noise

Structure preserving stochastic Runge–Kutta–Nyström methods for nonlinear second order stochastic differential equations with multiplicative noise

... To check the order conditions of the SRKN methods (2.2)–(2.4), one has to com- pare the expansion of the one-step solutions generated by the SRKN methods with the Stratonovich–Taylor expansion of the exact ... See full document

18

Closed form solution of an exponential kernel integral equation

Closed form solution of an exponential kernel integral equation

... Integral equations with this structure were encountered in the context of a stochastic differential equation model of solute transport in a porous medium (Kulasiri & Verwoerd, 2002), where ... See full document

5

Numerical methods for Stochastic differential equations: two examples

Numerical methods for Stochastic differential equations: two examples

... Stochastic Differential Equations (SDE in short) constrained in law have been introduced recently in their backward form by Briand, Elie and Hu in ...the path is reflected in order to ... See full document

13

Integral Inequality and Exponential Stability for Neutral Stochastic Partial Differential Equations with Delays

Integral Inequality and Exponential Stability for Neutral Stochastic Partial Differential Equations with Delays

... The aim of this paper is devoted to obtain some su ffi cient conditions for the exponential stability in p p ≥ 2-moment as well as almost surely exponential stability for mild solution of neutral stochastic partial ... See full document

15

Path-dependent backward stochastic Volterra integral equations with jumps, differentiability and duality principle

Path-dependent backward stochastic Volterra integral equations with jumps, differentiability and duality principle

... to path- dependent BSVIEs with jumps. Furthermore, we prove path-differentiability of this solution, where we use the functional Itˆo formula introduced by Dupire (2009) and extended by Cont and Fourni´e ... See full document

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