Runge–Kutta methods for jump–diffusion differential equations

Buckwar, Evelyn; Riedler, Martin

doi:10.1016/j.cam.2011.08.001

Cited by 27 publications

(23 citation statements)

References 29 publications

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“…Then, Buckwar and G. Riedler [20] proposed the Runge-Kutta second-order implicit scheme for solving SDEwJs.…”

Section: Scheme 2 (Wst2 Scheme) Assume the Initial Condition Xmentioning

confidence: 99%

“…There are [9] the weak or strong order 2.0 Taylor schemes and jump-adapted order 2.0 Taylor schemes. Moreover, the higher order of Runge-Kutta methods for jump-diffusion differential equations can be found in [20]. However, these numerical schemes include multiple stochastic integrals, which are difficult to accurately compute and simulate.…”

Section: Introductionmentioning

confidence: 99%

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A New Simplified Weak Second-Order Scheme for Solving Stochastic Differential Equations with Jumps

et al. 2021

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In this paper, we propose a new weak second-order numerical scheme for solving stochastic differential equations with jumps. By using trapezoidal rule and the integration-by-parts formula of Malliavin calculus, we theoretically prove that the numerical scheme has second-order convergence rate. To demonstrate the effectiveness and the second-order convergence rate, three numerical experiments are given.

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“…Then, Buckwar and G. Riedler [20] proposed the Runge-Kutta second-order implicit scheme for solving SDEwJs.…”

Section: Scheme 2 (Wst2 Scheme) Assume the Initial Condition Xmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A New Simplified Weak Second-Order Scheme for Solving Stochastic Differential Equations with Jumps

et al. 2021

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“…where ω g = ω gx ω gy ω gz T and ω = ω x ω y ω z T are the normalized gyroscope raw data and the corrected gyroscope data, respectively; K P and K I are the error control items, which are 2.0 and 0.001 in our research work, respectively. Then, the corrected gyroscope data should be substituted into the quaternion differential equation and the first-order Runge-Kutta method [45] is used to get the quaternion update equation as follows:…”

Section: A Pedestrian Dead Reckoningmentioning

confidence: 99%

Indoor Positioning Tightly Coupled Wi-Fi FTM Ranging and PDR Based on the Extended Kalman Filter for Smartphones

Sun

Wang

et al. 2020

IEEE Access

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The smartphone-based Wi-Fi fine time measurement (FTM) technique has provided a new approach for Wi-Fi-based indoor location on mobile phones since the 2018 release of the Google Android Pie system, which supports the IEEE 802.11-2016 protocol and can directly measure the distance between the initiator and the responder. This paper studies in detail the properties of mobile phone Wi-Fi ranging and positioning performance. Considering non-line-of-sight (NLOS) error identification, a real-time ranging error compensation model based on the least-squares (LS) method and an adaptive Wi-Fi FTM positioning algorithm (AWFP) utilizing the weighted least-squares (WLS) method are devised. To improve accuracy, a new tightly coupled fusion positioning algorithm integrating Wi-Fi FTM and built-in mobile phone sensors based on the extended Kalman filter (EKF) is constructed. The experimental results show that the ranging precision and Wi-Fi positioning accuracy are improved. Based on the high-precision Wi-Fi ranging and positioning results, the final location accuracy of the proposed fusion method is 0.98 m, and the root-meansquare error (RMSE) is 1.10 m, which are better than those of the PDR, Wi-Fi FTM and loosely coupled PDR/Wi-Fi FTM integration based on the EKF. INDEX TERMS Indoor positioning, Wi-Fi FTM, pedestrian dead reckoning, tightly coupled, ekf.

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“…There are some scholars studying in higher order weak numerical schemes for solving SDEwJ. For example, Buckwar [21] proposed the implicit order 2.0 Runge-Kutta scheme for solving jump-diffusion differential equations. Liu and Li [22] studied an effective higher order weak scheme to solve stochastic differential equations with jumps but involved computing multiple stochastic integral.…”

Section: Introductionmentioning

confidence: 99%

“…Inspired by high-order numerical methods [21][22][23] and based on classical weak order 2.0 Taylor scheme [24] for solving stochastic differential equations, we develop a new weak order 2.0 numerical approximation scheme for solving SDEwMS and rigorously prove the new scheme has order 2.0 convergence rate by using Malliavin stochastic analysis. Meanwhile, we simply utilize the Runge-Kutta scheme for solving SDEwMS in order to make a comparison with the new scheme on the accuracy and convergence rate.…”

Section: Introductionmentioning

confidence: 99%

A High Order Accurate and Effective Scheme for Solving Markovian Switching Stochastic Models

Yang¹,

Feng²,

Wang³

et al. 2021

Mathematics

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In this paper, we propose a new weak order 2.0 numerical scheme for solving stochastic differential equations with Markovian switching (SDEwMS). Using the Malliavin stochastic analysis, we theoretically prove that the new scheme has local weak order 3.0 convergence rate. Combining the special property of Markov chain, we study the effects from the changes of state space on the convergence rate of the new scheme. Two numerical experiments are given to verify the theoretical results.

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Runge–Kutta methods for jump–diffusion differential equations

Cited by 27 publications

References 29 publications

A New Simplified Weak Second-Order Scheme for Solving Stochastic Differential Equations with Jumps

A New Simplified Weak Second-Order Scheme for Solving Stochastic Differential Equations with Jumps

Indoor Positioning Tightly Coupled Wi-Fi FTM Ranging and PDR Based on the Extended Kalman Filter for Smartphones

A High Order Accurate and Effective Scheme for Solving Markovian Switching Stochastic Models

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