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Convergence of numerical solution to stochastic delay differential equation with Poisson jump and Markovian switching

Li Ronghua, Chang Zhaoguang
2007 Applied Mathematics and Computation  
This paper is concerned with the Euler-Maruyama approximate solution of nonlinear stochastic delay differential equations with Markovian switching (SDDEwMSs).  ...  We establish the existence and uniqueness results for the global solution of SDDEwMSs under the polynomial growth and the local Lipschitz condition. we then introduce Euler-Maruyama approximate solution  ...  For the similar result of highly nonlinear neutral stochastic delay differential equations (NSDDEs) with time-dependent delay, please see Milosevic [6] .  ... 
doi:10.1016/j.amc.2006.06.112 fatcat:oohbqefyjbfghku2dhdvl3tazq

Almost sure exponential stability of the θ-Euler-Maruyama method for neutral stochastic differential equations with time-dependent delay when θ ∈ [0; 1 2]

Maja Obradovic, Marija Milosevic
2017 Filomat  
Milošević, Almost sure exponential stability of solutions to highly nonlinear neutral stochastics differential equations with time-dependent delay and Euler-Maruyama approximation, Math. Comput.  ...  differential equations with time-dependent delay.  ...  The subject of this paper is consideration of the θ-Euler-Maruyama method, when θ ∈ [0, 1 2 ] , for a class of neutral stochastic differential equations with time-dependent delay under the linear growth  ... 
doi:10.2298/fil1718629o fatcat:i6a3npuje5aazo7utytpva7bsi

Nonlinear Analysis of Dynamical Complex Networks

Zidong Wang, Bo Shen, Hongli Dong, Jun Hu
2013 Abstract and Applied Analysis  
Complex networks are composed of a large number of highly interconnected dynamical units and therefore exhibit very complicated dynamics.  ...  Since the introduction of the small-world network principle, a great deal of research has been focused on the dependence of the asymptotic behavior of interconnected oscillatory agents on the structural  ...  Acknowledgments This special issue is a timely reflection of the research progress in the area of nonlinear analysis of dynamical complex networks.  ... 
doi:10.1155/2013/530124 fatcat:k2qk6lytnvdcdlkjq6mpga7pya

The truncated Euler-Maruyama method for highly nonlinear neutral stochastic differential equations with time-dependent delay

Aleksandra Petrovic, Marija Milosevic
2021 Filomat  
The main goal of this paper is to establish the Lq-convergence of the truncated Euler-Maruyama method for neutral stochastic differential equations with time-dependent delay under the Khasminskii-type  ...  Since the main result is related to the Lq-convergence of the Euler-Maruyama method under the global Lipschitz condition on the coefficients of the equation under consideration, for completeness of the  ...  Acknowledgement: The authors are very thankful to the reviewers for their valuable suggestions which improved the paper.  ... 
doi:10.2298/fil2107457p fatcat:i5a4hwusuvg6tjr35ooc7clmv4

subject index volumes 201 to 210

2007 Journal of Computational and Applied Mathematics  
Time-delay systems 206 366 Time-dependent evolution equation 204 159, 172 Time-harmonic scattering problem 204 440 Time-splitting spectral method 205 88 Time-stepping schemes 204 95 Time-varying discrete  ...  205 479 Delay differential equation 201 55, 348 Delay partial differential equations 205 552 Delay-dependence 206 366 Delays 206 293 Derivative approximation 205 239 Derivative-free 203 57; 206  ... 
doi:10.1016/s0377-0427(07)00502-x fatcat:tovvilkoczetvl423gcjxug7gm

Exponential Stability of Highly Nonlinear Neutral Pantograph Stochastic Differential Equations

Mingxuan Shen, Weiyin Fei, Xuerong Mao, Shounian Deng
2018 Asian journal of control  
In this paper, we investigate the exponential stability of highly nonlinear hybrid neutral pantograph stochastic differential equations(NPSDEs).  ...  The methods of Lyapunov functions and M-matrix are used to study exponential stability and boundedness of the hybrid NPSDEs.  ...  INTRODUCTION Stochastic delay differential equations are widely used to model stochastic systems whose evolution depends on past history of the state.  ... 
doi:10.1002/asjc.1903 fatcat:5ikntdtffjcexhncm7ychf6cwi

Numerical method of highly nonlinear and nonautonomous neutral stochastic differential delay equations with Markovian switching

Shuaibin Gao, Junhao Hu
2020 Advances in Difference Equations  
AbstractIn this paper, we establish a partially truncated EulerMaruyama scheme for highly nonlinear and nonautonomous neutral stochastic differential delay equations with Markovian switching.  ...  We investigate the strong convergence rate and almost sure exponential stability of the numerical solutions under the generalized Khasminskii-type condition.  ...  Funding This work is supported by the National Natural Science Foundation of China (Grant Nos. 61876192 and 62076106) and the Fundamental Research Funds for the Central Universities of South-Central University  ... 
doi:10.1186/s13662-020-03113-x fatcat:b4xehc5lfbhybdt4i6cvbomn6y

Convergence rate of Euler–Maruyama scheme for SDDEs of neutral type

Yanting Ji
2021 Journal of Inequalities and Applications  
AbstractIn this paper, we are concerned with the convergence rate of EulerMaruyama (EM) scheme for stochastic differential delay equations (SDDEs) of neutral type, where the neutral, drift, and diffusion  ...  More precisely, for SDDEs of neutral type driven by Brownian motions, we reveal that the convergence rate of the corresponding EM scheme is one-half; Whereas for SDDEs of neutral type driven by pure jump  ...  Meanwhile, the author acknowledges Ms Ruoyu Zhang and Mr Yi Yang for their advice in the numerical simulation. Funding Not applicable. Availability of data and materials Not applicable.  ... 
doi:10.1186/s13660-020-02533-3 fatcat:2nenrykikvhjpaqyje6cb5m4sm

Author Index Volume 235 (2011)

2011 Journal of Computational and Applied Mathematics  
Zhang, The stability of neutral stochastic delay differential equations with Poisson jumps by fixed points 3115-3120 Liu, Y.-C., J. Zhang and G.-H.  ...  Li, A penalty finite element method based on the Euler implicit/explicit scheme for the time-dependent Navier-Stokes equations 708-725 He, Q., see Fan, M. 91-101 Hernández, E., D. Kalise and E.  ... 
doi:10.1016/s0377-0427(11)00383-9 fatcat:iydszqpkezgivirtbnwhpwere4

Stochastic Simulation for Spatial Modelling of Dynamic Processes in a Living Cell [chapter]

Kevin Burrage, Pamela M. Burrage, André Leier, Tatiana Marquez-Lago, Dan V. Nicolau
2011 Design and Analysis of Biomolecular Circuits  
This chapter gives an overview of the state of the art in the development of stochastic simulation techniques for the spatial modelling of dynamic processes in a living cell.  ...  These processes are often so complicated that purely temporal mathematical models cannot adequately capture the complex chemical kinetics and transport processes of, for example, proteins or vesicles.  ...  Various numerical methods can then be applied to this equation -the simplest method being the Euler-Maruyama method [37] . These temporal approaches are applied under the principle of homogeneity.  ... 
doi:10.1007/978-1-4419-6766-4_2 fatcat:tdedncl22rayfnsoefyoe23y2m

Stability with general decay rate of hybrid neutral stochastic pantograph differential equations driven by Lévy noise

Tian Zhang, Chuanhou Gao
2021 Discrete and continuous dynamical systems. Series B  
decay rate (including exponential decay, polynomial decay, and logarithmic decay) of highly nonlinear hybrid neutral stochastic pantograph differential equations driven by L<inline-formula><tex-math id  ...  NSPDEs-LN with highly nonlinear coefficients.  ...  The authors would like to thank the editor and the reviewers for their valuable comments and suggestions, which can deeply enhance the quality of our work.  ... 
doi:10.3934/dcdsb.2021204 fatcat:2bkxl343bvgafb6mtp34e2h2v4

On the asymptotic stability and numerical analysis of solutions to nonlinear stochastic differential equations with jumps

Wei Mao, Surong You, Xuerong Mao
2016 Journal of Computational and Applied Mathematics  
Acknowledgements The authors would like to thank the referees for their valuable comments and suggestions.  ...  The authors would also like to thank the Royal Society of Edinburgh, the National Natural Science  ...  Milosevic [22] studied the numerical solution of highly nonlinear neutral SDEs with time-dependent delay under the Khasminskhii-type conditions.  ... 
doi:10.1016/j.cam.2016.01.020 fatcat:mafwk3whpfayvlqzy6nvhdkwne

Convergence of Numerical Solution of The Tamed Milstein Method for NSDDEs [article]

Qiquan Fan, Yingxiao Min, Yingying Wang, Yanting Ji
2022 arXiv   pre-print
In this paper, we apply the tamed technique to the Milstein numerical scheme to investigate Neutral Stochastic Delay Differential Equations(NSDDEs) with highly nonlinear coefficients.  ...  Under the local Lipschitz condition and Khasminskii condition, the tamed Milstein numerical solution converges strongly to the exact solution.  ...  Introduction As an important class of differential dynamical systems, Neutral Stochastic Delay Differential Equations(NSDDEs) play an important role in many fields, such as biology, finance and automatic  ... 
arXiv:2203.06627v1 fatcat:wtndxp5brjdcvgzf3odrihcvtm

Determinants of Brain Rhythm Burst Statistics

Arthur S. Powanwe, André Longtin
2019 Scientific Reports  
Using the stochastic averaging method, we derive dynamics for the phase and envelope of the amplitude process, and find that they depend on only two meta-parameters that combine all the model parameters  ...  The probability density for the rhythm's envelope as well as the mean burst duration are then derived using first passage time analysis.  ...  Author contributions A.S.P. and A.L. conceived the study, A.S.P. performed all the research, analysed the results and wrote the initial draft. A.S.P. and A.L. reviewed and revised the manuscript.  ... 
doi:10.1038/s41598-019-54444-z pmid:31797877 pmcid:PMC6892937 fatcat:ssmzcujsove4xmk7aevuersptu

A Review of Complex Systems Approaches to Cancer Networks [article]

Abicumaran Uthamacumaran
2020 arXiv   pre-print
The emerging field of complex systems has redefined cancer networks as a computational system with intractable algorithmic complexity.  ...  Cancer cell decision-making is investigated within the framework of complex systems and complexity theory.  ...  To simulate dynamic trajectories, the 1 st order Runge-Kutta finite difference method is used to solve the updating of neurons (genes) as an ordinary differential equation while the Euler-Maruyama method  ... 
arXiv:2009.12693v2 fatcat:kt3e4bqaufgwlbhx2wbgzftnpe
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