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[PDF] Top 20 Simultaneaous approximation of a family of (stochastic) differential equations

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Simultaneaous approximation of a family of (stochastic) differential equations

Simultaneaous approximation of a family of (stochastic) differential equations

... To approximatethe fractionalintegralof order a in (0,1), we use an integral representationbased on exponentialfunctionsintroducedin a previous paper, and we present a scheme to approxima[r] ... See full document

6

Stochastic differential equations and integrating factor

Stochastic differential equations and integrating factor

... The aim of this paper is the analytical solutions the family of first-order nonlinear stochastic differ- ential equations. We define an integrating factor for the large class of special nonlinear ... See full document

6

Stochastic Runge-Kutta method for stochastic delay differential equations

Stochastic Runge-Kutta method for stochastic delay differential equations

... solving SDDEs in various fields. It can also be shown in this research, the SRK methods are easy to implement compare to the approximation methods obtained from the truncating stochastic Taylor expansion. ... 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

... We develop a framework that allows the use of the multi-level Monte Carlo (MLMC) methodology (Giles in Acta Numer. 24:259–328, 2015. https://doi.org/10.1017/S096249291500001X) to calculate expectations with respect to ... See full document

18

Improved bridge constructs for stochastic differential equations

Improved bridge constructs for stochastic differential equations

... the process into a deterministic part that accounts for forward dynamics, and a residual stochastic process. The intractable end-point conditioned residual SDE is approximated using the modified diffusion bridge ... See full document

16

Asymptotic boundedness and stability of solutions to hybrid stochastic differential equations with jumps and the Euler-Maruyama approximation

Asymptotic boundedness and stability of solutions to hybrid stochastic differential equations with jumps and the Euler-Maruyama approximation

... 12 4 5 6 7 8 9 10 13 14 15 16 17 Convergence analysis of the EM approximate solutions In this section, we will study the convergence of the EM approximate solutions for hybrid SDEs with [r] ... See full document

33

Stability of stochastic differential equations in infinite dimensions

Stability of stochastic differential equations in infinite dimensions

... to stochastic differential equations with Markovian ...of stochastic differential equations has always lain at the center of our understanding concerning stochastic models ... See full document

203

A Partial-differential Approximation for Spatial Stochastic Process Algebra

A Partial-differential Approximation for Spatial Stochastic Process Algebra

... We study a spatial framework for process algebra with or- dinary differential equation (ODE) semantics. We consider an explicit mobility model over a 2D lattice where processes may walk to neighbouring regions ... See full document

8

Stochastic control representations for penalized backward stochastic differential equations

Stochastic control representations for penalized backward stochastic differential equations

... Thanks to our optimal stopping representation, the penalized BSDE (1.3) is noth- ing but a random time discretization of the optimal stopping representation for the corresponding reflected BSDE (1.1), where the time is ... See full document

25

On constrained Langevin equations and (bio)chemical reaction networks

On constrained Langevin equations and (bio)chemical reaction networks

... deterministic differential equations representing the time evolution of molecular ...mentally stochastic in ...field approximation to these systems and are generally good predictors when the ... See full document

30

Backward stochastic differential equations with Young drift

Backward stochastic differential equations with Young drift

... Here η has finite q-variation, with q ∈ [ 1 , 2 ) and the last term is a priori not well-defined. There are several approaches to make sense of such a “rough” PDE (or pathwise SPDEs). We shall employ the solution concept ... See full document

17

Strong approximation for Itô stochastic differential equations

Strong approximation for Itô stochastic differential equations

... ordinary differential equations ...few equations, the study of numerical methods have become more important and these must be designed to be implemented with a certain order of ... See full document

13

Path Integral Methods for Stochastic Differential Equations

Path Integral Methods for Stochastic Differential Equations

... “classical” equations of motion (mean field theory in statistical ...semiclassical approximation. In both quantum mechanics and stochastic analysis this is also known as a WKB ... See full document

35

Analysis of the stability and convergence of a finite difference approximation for stochastic partial differential equations

Analysis of the stability and convergence of a finite difference approximation for stochastic partial differential equations

... finite difference scheme (2.6) the increments of Wiener process are independent of the state u n k . Essentially, it is important for the solution of stochastic difference scheme to converge to the solution of the ... See full document

25

Successive approximation of solutions to doubly perturbed stochastic differential equations with jumps

Successive approximation of solutions to doubly perturbed stochastic differential equations with jumps

... | b ( t, x ) − b ( t, y )| ≤ ρ (| x − y |) . (1.5) From the analysis of Section 5, the coefficients of equation (1.3) do not satisfy the global Lip- schitz condition [8] or non-Lipschitz condition [9, 10]. In other ... See full document

19

Taylor approximation of stochastic functional differential equations with the Poisson jump

Taylor approximation of stochastic functional differential equations with the Poisson jump

... of stochastic functional differential delay equations with the Poisson jump, whose coefficients are general Taylor expansions of the coefficients of the initial ...of stochastic differential ...of ... See full document

10

Finite Difference Approximation for Linear Stochastic Partial Differential Equations with Method of Lines

Finite Difference Approximation for Linear Stochastic Partial Differential Equations with Method of Lines

... ence approximation of the boundary value solutions for two broad classes of linear SPDEs, the linear elliptic and parabolic ...the approximation method works by transforming the SPDE to a system of ... See full document

19

Uncertainty propagation and quantification in a continuous time dynamical system

Uncertainty propagation and quantification in a continuous time dynamical system

... with stochastic processes, which can be obtained due to the variability/stochasticity in the growth rate and/or variability in the initial ...the stochastic processes with which those nonlinear structured ... See full document

45

On the Effects of Different Interpretations of Stochastic Differential Equations

On the Effects of Different Interpretations of Stochastic Differential Equations

... DOI: 10.4236/am.2019.1011063 877 Applied Mathematics tremely irregular random force, the so-called white noise, a Gaussian process because of the central limit theorem. In this way, the displacement X ( t ) of the ... See full document

16

Almost sure exponential stability of an explicit stochastic orthogonal Runge Kutta Chebyshev method for stochastic delay differential equations

Almost sure exponential stability of an explicit stochastic orthogonal Runge Kutta Chebyshev method for stochastic delay differential equations

... To the best knowledge of authors, there is no similar result about almost sure stabil- ity of Runge-Kutta type methods for SDDEs, and nearly all existing results concerned with Euler-Maruyama type schemes. Recently, ... See full document

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