Introduction to Stochastic Time Discrete Approximation

Kloeden, Peter E.; Platen, Eckhard

doi:10.1007/978-3-662-12616-5_9

Cited by 3 publications

(4 citation statements)

References 94 publications

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“…The potential applications of the Stratonovich differential are autonomous systems, hydrology and mechanics, non-linear dynamic circuits etc. (see Kloeden and Platten, 1992: 264). In this paper, two appealing structures of Stratonovich bilinear stochastic differential equations are the subject of investigations in filtering contexts.…”

Section: Problem Formulationmentioning

confidence: 98%

“…Here, we explain bilinear stochastic differential systems. After accounting for random forcing terms in the system parameters of the ordinary differential equation, where the random input-state coupling term arises, we arrive at the bilinear stochastic differential equation, for example, the helicopter rotor dynamics (Kloeden and Platten, 1992: 261). The structure of a scalar bilinear stochastic differential equation (Patil and Sharma, 2014; Terdik, 1990) is…”

Section: Introductionmentioning

confidence: 99%

“…The stochastic differential equation with 1 2 - differential is the Stratonovich stochastic differential equation. Notably, Stratonovich stochastic differential equations have found their striking applications in structural dynamics, hydrology, Helicopter rotor dynamics, satellite orbital stability, nemantic liquid crystal and fatigue cracking (see Kloeden and Platen, 1992: 264). Furthermore, the Stratonovich ‘bilinear’ stochastic differential equations have found applications in appealing practical problems, switched electrical networks and circuits, and helicopter rotor dynamics (see Kloeden and Platen, 1992: 261; and Terdik, 1990).…”

Section: Introductionmentioning

confidence: 99%

“…Notably, Stratonovich stochastic differential equations have found their striking applications in structural dynamics, hydrology, Helicopter rotor dynamics, satellite orbital stability, nemantic liquid crystal and fatigue cracking (see Kloeden and Platen, 1992: 264). Furthermore, the Stratonovich ‘bilinear’ stochastic differential equations have found applications in appealing practical problems, switched electrical networks and circuits, and helicopter rotor dynamics (see Kloeden and Platen, 1992: 261; and Terdik, 1990). Despite fecundity of bilinear stochastic differential equations in real physical systems, consensus on the Itô–Stratonovich dilemma (Mannella and McClintock, 2012), filtering of bilinear systems ‘embedded in the Stratonovich stochasticity’ remains unexplored.…”

Section: Introductionmentioning

confidence: 99%

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Non-linear filtering for bilinear stochastic differential systems: A Stratonovich perspective

Rathore

Sharma

Bhatt

et al. 2020

Transactions of the Institute of Measurement and Control

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Bilinear stochastic differential equations have found applications to model turbulence in autonomous systems as well as switching uncertainty in non-linear dynamic circuits. In signal processing and control literature, bilinear stochastic differential equations are ubiquitous, since they capture non-linear qualitative characteristics of dynamic systems as well as offer closed-form solutions. The novelties of the paper are two: we weave bilinear filtering for the Stratonovich stochasticity. Then this paper unfolds the usefulness of bilinear filtering for switched dynamic systems. First, the Stratonovich stochasticity is embedded into a vector ‘bilinear’ time-varying stochastic differential equations. Then, coupled non-linear filtering equations are achieved. Finally, the non-linear filtering results are applied to an appealing bilinear stochastic Ćuk converter circuit. This paper also encompasses a system of coupled bilinear filtering equations for the vector input Brownian motion case. This paper brings the notions of systems theory, that is, bilinearity, Stratonovich stochasticity, non-linear filtering techniques and switched electrical networks together. Numerical simulation results are presented to demonstrate that the proposed bilinear filter can achieve much better and accurate filtering performance than the conventional Extended Kalman Filter (EKF).

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Section: Problem Formulationmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Non-linear filtering for bilinear stochastic differential systems: A Stratonovich perspective

Rathore

Sharma

Bhatt

et al. 2020

Transactions of the Institute of Measurement and Control

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Multilevel Monte Carlo method for the Brownian configuration field of polymer fluids

Hou

et al. 2020

AIP Advances

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Stochastic Brownian dynamics is an extremely powerful way to simulate the polymer dynamics in solutions and melts. Mathematically, these models are described by stochastic differential equations. The most challenging problems are the Monte Carlo algorithm, which simulates the motion of a large number of model particles and hence requires an enormous amount of computer time. It is therefore necessary to develop an efficient numerical method in operational emergency response applications. In this paper, we give an improved multilevel Monte Carlo (improved-MLMC) method based on equilibrium control variables at each level to calculate the propagation of polymers. The improved-MLMC method can be shown to result in asymptotically optimal random errors and reduce total cost when compared to the standard Monte Carlo and MLMC methods. Finally, the effect of the Wi number (dimensionless parameter) on the total cost of the presented MLMC method is also discussed in detail.

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A comparison of three algorithms in the filtering of a Markov-modulated non-homogeneous Poisson process

Li,

Mamon

2024

International Journal of Systems Science

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Introduction to Stochastic Time Discrete Approximation

Cited by 3 publications

References 94 publications

Non-linear filtering for bilinear stochastic differential systems: A Stratonovich perspective

Non-linear filtering for bilinear stochastic differential systems: A Stratonovich perspective

Multilevel Monte Carlo method for the Brownian configuration field of polymer fluids

A comparison of three algorithms in the filtering of a Markov-modulated non-homogeneous Poisson process

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