Caustic Frequency in 2D Stochastic Flows Modeling Turbulence by Leonid I. Piterbarg

“…First, a system of nonlinear stochastic differential equations involving the Jacobian is derived and reduced to a smaller number of unknowns. …”
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Rectified deep neural networks overcome the curse of dimensionality for nonsmooth value functions in zero-sum games of nonlinear stiff systems by Reisinger, C, Zhang, Y

“…In this paper, we establish that for a wide class of controlled stochastic differential equations (SDEs) with stiff coefficients, the value functions of corresponding zero-sum games can be represented by a deep artificial neural network (DNN), whose complexity grows at most polynomially in both the dimension of the state equation and the reciprocal of the required accuracy. …”

Error bounds for flow matching methods by Benton, J, Deligiannidis, G, Doucet, A

“…<p>Score-based generative models are a popular class of generative modelling techniques relying on stochastic differential equations (SDE). From their inception, it was realized that it was also possible to perform generation using ordinary differential equations (ODE) rather than SDE. …”

Linear convergence of a policy gradient method for some finite horizon continuous time control problems by Reisinger, C, Stockinger, W, Zhang, Y

“…The proof exploits careful regularity estimates of backward stochastic differential equations.…”

A non-linear stochastic model for an office building with air infiltration by Anders Thavlov, Henrik Madsen

“…The models are formulated using stochastic differential equations and the model parameters are estimated using a maximum-likelihood technique. …”
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A Transverse Hamiltonian Approach to Infinitesimal Perturbation Analysis of Quantum Stochastic Systems by Igor G. Vladimirov

“…This paper is concerned with variational methods for open quantum systems with Markovian dynamics governed by Hudson–Parthasarathy quantum stochastic differential equations. These QSDEs are driven by quantum Wiener processes of the external bosonic fields and are specified by the system Hamiltonian and system–field coupling operators. …”
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Quantum dynamics of nonlinear excitations in the Ablowitz-Ladik model by Umarov, Bakhram

“…In this method the evolution equation for quantum density operator is converted to the partial differential equation for some classical quasi-distribution function, which in some cases can be reduced to the system of ordinary stochastic differential equations. In this paper we are presenting the results of the investigation of quantum Ablowitz-Ladik model by the phase space representation methods. …”
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An optimal polynomial approximation of Brownian motion by Foster, J, Lyons, T, Oberhauser, H

“…In addition, discretizing Brownian paths as piecewise parabolas gives a locally higher order numerical method for stochastic differential equations (SDEs) when compared to the piecewise linear approach. …”

Modeling and copying human head movements by Heuring, J, Murray, D

“…This paper derives two discrete motion models for three-dimensional (3-D) pose recovery starting from the stochastic differential equations that describe the object's motion in continuous time. …”

3D mobility models and analysis for UAVs by Smith, PJ, Dmochowski, PA, Singh, I, Green, R, Dettmann, CP, Coon, JP

“…Based on stochastic differential equations, the models offer a unique property of explicitly incorporating the mobility control mechanism and environmental perturbation, while enabling tractable steady state solutions for properties such as position and connectivity. …”

Control mechanisms for mobile devices by Smith, PJ, Singh, I, Dmochowski, P, Dettmann, CP, Coon, JP

“…For this scenario, we construct stochastic differential equations for the mobility process and solve for the steady state probability density function of displacement. …”

Well-posedness and numerical schemes for one-dimensional McKean-Vlasov equations and interacting particle systems with discontinuous drift by Leobacher, G, Reisinger, C, Stockinger, W

“…In this paper, we first establish well-posedness results for one-dimensional McKean–Vlasov stochastic differential equations (SDEs) and related particle systems with a measure-dependent drift coefficient that is discontinuous in the spatial component, and a diffusion coefficient which is a Lipschitz function of the state only. …”

Quantum omega-semimartingales and stochastic evolutions by Belton, A

“…We consider quantum stochastic differential equations with bounded, <em>omega</em>-adapted coefficients that are time dependent and act on the whole Fock space. …”

Well-posedness and tamed schemes for McKean-Vlasov equations with common noise by Kumar, C, Neelima, Reisinger, C, Stockinger, W

“…In this paper, we first establish well-posedness of McKean–Vlasov stochastic differential equations (McKean–Vlasov SDEs) with common noise, possibly with coefficients of super-linear growth in the state variable. …”

Smooth random functions, random ODEs, and Gaussian processes by Filip, S, Javeed, A, Trefethen, L

“…For example, one can solve smooth random ordinary differential equations using standard mathematical definitions and numerical algorithms, rather than having to develop new definitions and algorithms of stochastic differential equations. In the limit as the number of Fourier coefficients defining a smooth random function goes to $\infty$, one obtains the usual stochastic objects in what is known as their Stratonovich interpretation.…”

A stochastic model for the turbulent ocean heat flux under Arctic sea ice by Toppaladoddi, S, Wells, AJ

“…Here, we develop a model of the turbulent ice-ocean heat flux using coupled ordinary stochastic differential equations to model fluctuations in the vertical velocity and temperature in the Arctic mixed layer. …”

Stochastic Small Signal Stability of a Power System with Uncertainties by Yan Xu, Fushuan Wen, Hongwei Zhao, Minghui Chen, Zeng Yang, Huiyu Shang

“…The power system is modeled as a set of stochastic differential equations (SDEs). The supremum of the norm of the covariance is employed to characterize the influence of magnitudes of uncertainties on the power system. …”
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Parameter Estimation of the Heston Volatility Model with Jumps in the Asset Prices by Jarosław Gruszka , Janusz Szwabiński

“…The parametric estimation of stochastic differential equations (SDEs) has been the subject of intense studies already for several decades. …”
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PPDONet: Deep Operator Networks for Fast Prediction of Steady-state Solutions in Disk–Planet Systems by Shunyuan Mao, Ruobing Dong, Lu Lu, Kwang Moo Yi, Sifan Wang, Paris Perdikaris

“…We base our tool on Deep Operator Networks, a class of neural networks capable of learning nonlinear operators to represent deterministic and stochastic differential equations. With PPDONet we map three scalar parameters in a disk–planet system—the Shakura–Sunyaev viscosity α , the disk aspect ratio h _0 , and the planet–star mass ratio q —to steady-state solutions of the disk surface density, radial velocity, and azimuthal velocity. …”
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Stability Assessment of Stochastic Differential-Algebraic Systems via Lyapunov Exponents with an Application to Power Systems by Andrés González-Zumba, Pedro Fernández-de-Córdoba, Juan-Carlos Cortés, Volker Mehrmann

“…We focus on index-1 SDAEs and their reformulation as ordinary stochastic differential equations (SDEs). Via ergodic theory, it is then feasible to analyze the LEs via the random dynamical system generated by the underlying SDEs. …”
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