Drift Coefficients Research Articles

An explicit Milstein-type scheme for interacting particle systems and McKean–Vlasov SDEs with common noise and non-differentiable drift coefficients

An explicit Milstein-type scheme for interacting particle systems and McKean–Vlasov SDEs with common noise and non-differentiable drift coefficients

Controlled Reflected McKean–Vlasov SDEs and Neumann Problem for Backward SPDEs

This paper is concerned with the stochastic optimal control problem of a 1-dimensional McKean–Vlasov stochastic differential equation (SDE) with reflection, of which the drift coefficient and diffusion coefficient can be both dependent on the state of the solution process along with its law and control. One backward stochastic partial differential equation (BSPDE) with the Neumann boundary condition can represent the value function of this control problem. Existence and uniqueness of the solution to the above equation are obtained. Finally, the optimal feedback control can be constructed by the BSPDE.

Dynamics of inertial particles under velocity resetting

We investigate stochastic resetting in coupled systems involving two degrees of freedom, where only one variable is reset. The resetting variable, which we think of as hidden, indirectly affects the remaining observable variable via correlations. We derive the Fourier–Laplace transforms of the observable variable’s propagator and provide a recursive relation for all the moments, facilitating a comprehensive examination of the process. We apply this framework to inertial transport processes where we observe the particle position while the velocity is hidden and is being reset at a constant rate. We show that velocity resetting results in a linearly growing spatial mean squared displacement at later times, independently of reset-free dynamics, due to resetting-induced tempering of velocity correlations. General expressions for the effective diffusion and drift coefficients are derived as a function of the resetting rate. A non-trivial dependence on the rate may appear due to multiple timescales and crossovers in the reset-free dynamics. An extension that incorporates refractory periods after each reset is considered, where post-resetting pauses can lead to anomalous diffusive behavior. Our results are of relevance to a wide range of systems, such as inertial transport where the mechanical momentum is lost in collisions with the environment or the behavior of living organisms where stop-and-go locomotion with inertia is ubiquitous. Numerical simulations for underdamped Brownian motion and the random acceleration process confirm our findings.

Improvement of Multilevel Memory Performance of MnTe Thin Films by Ta Doping.

The pressing need for data storage in the era of big data has driven the development of new storage technologies. As a prominent contender for next-generation memory, phase-change memory can effectively increase storage density through multilevel cell operation and can be applied to neuromorphic and in-memory computing. Herein, the structure and properties of Ta-doped MnTe thin films and their inherent correlations are systematically investigated. Amorphous MnTe thin films sequentially precipitated cubic MnTe2 and hexagonal Te phases with increasing temperature, causing resistance changes. Ta doping inhibited phase segregation in the films and improved their thermal stability in the amorphous state. A phase-change memory cell based on a Ta2.8%-MnTe thin film exhibited three stable resistive states with low resistive drift coefficients. The study findings reveal the possibility of regulating the two-step phase-change process in Ta-MnTe thin films, providing insight into the design of multilevel phase-change memory.

A higher-order approximation method for jump-diffusion SDEs with a discontinuous drift coefficient

We present the first higher-order approximation scheme for solutions of jump-diffusion stochastic differential equations with discontinuous drift. For this transformation-based jump-adapted quasi-Milstein scheme, we prove Lp-convergence order 3/4. To obtain this result, we prove that under slightly stronger assumptions (but still weaker than assumptions applied before) a related jump-adapted quasi-Milstein scheme has convergence order 3/4; in a special case it even has convergence order 1. Order 3/4 is conjectured to be optimal.

Asymptotic properties for the parameter estimation in stochastic (functional) differential equations with Hölder drift

In this paper, by taking Zvonkin's transformation, we investigate parameter estimation for a class of multidimensional stochastic differential equations with small perturbation parameters in diffusion coefficients, where the drift coefficients not only have an unknown parameter θ but also are Hölder continuous. These processes may enhance the applicability of our results to considerable practical models. Due to the irregular drift, the primary challenge is dealing with the mean square error between an accurate and numerical solution. Under these settings, we demonstrate the consistency and asymptotic normality of error concerning the least squares estimator in probability when stepsize δ → 0 and small parameter ε → 0 simultaneously. Moreover, we extend the results to the case of stochastic functional differential equations.

Convergence analysis of an explicit method and its random batch approximation for the McKean–Vlasov equations with non-globally Lipschitz conditions

In this paper, we present a numerical approach to solve the McKean–Vlasov equations, which are distribution-dependent stochastic differential equations, under some non-globally Lipschitz conditions for both the drift and diffusion coefficients. We establish a propagation of chaos result, based on which the McKean–Vlasov equation is approximated by an interacting particle system. A truncated Euler scheme is then proposed for the interacting particle system allowing for a Khasminskii- type condition on the coefficients. To reduce the computational cost, the random batch approximation proposed in [S. Jin, L. Li and J. Liu, J. Comput. Phys. 400 (2020) 108877.] is extended to the interacting particle system where the interaction could take place in the diffusion term. An almost half order of convergence is proved in Lp sense. Numerical tests are performed to verify the theoretical results.

The study on application of high-order tilted asymmetric Bragg gratings in quantum cascade lasers

High-order gratings eliminate the need for high-resolution lithography in the definition process. However, they are not widely adopted due to inability to provide sufficient coupling coefficients in long-wave mid-infrared quantum cascade lasers (QCLs). Fifth order tilted asymmetric gratings (TAS-gratings) distributed feedback (DFB) QCLs with stable single longitudinal mode are firstly reported in this paper. TAS-gratings exhibit longitudinal mode selection capability across a broad range of asymmetric distances around 1.18 μm and duty cycles around 0.5, which is attributed to their larger effective duty cycles and phase differences caused by an 18° tilt angle of the grating in the middle and two asymmetrical distributions of gratings on both sides. Further experimental results indicate that DFB QCLs with TAS-gratings exhibit stable excitation of single longitudinal modes within the duty cycle range of 0.48–0.54 due to the large coupling coefficients, the temperature drift coefficient of 0.29 nm/K of TAS-grating device is reduced by 64% compared with symmetric gratings (S-gratings) devices, the maximum side-mode suppression ratio (SMSR) of the devices exceeds 25 dB. TAS-gratings offer greater process tolerance, design flexibility and lower preparation difficulty. This study provides a solution to achieve sufficiently large coupling coefficients for high-order gratings applied to long-wave mid-infrared QCLs.

Narrow-linewidth stable-spectrum diode laser source basing on polarization-separated external cavity feedback technology

In this study, we propose a polarization-separated external cavity feedback structure based on a volume Bragg grating (VBG) that folds the optical path of a free-running diode laser into a non-straight direction for linewidth narrowing and central wavelength locking. By employing diode laser polarization splitting technology and external cavity feedback technology, a similar output power and narrow linewidth but a smaller current drift coefficient of central wavelength are demonstrated by comparing with the standard straight external cavity feedback structure. Experimental results show that the current drift coefficient of central wavelength reduce to 1/5 that of the traditional method. According to our research, this is the first report on folding the extended external cavity feedback optical path in a non-straight direction basing on polarization splitting technology, providing a new method for external cavity feedback based on the VBG.

Nonequilibrium solvent response force: What happens if you push a Brownian particle

In this Letter we discuss how to add forces to the Langevin equation. We derive an exact generalized Langevin equation for the dynamics of one particle subject to an external force embedded in a system of many interacting particles. The external force may depend on time and/or on the phase-space coordinates of the system. We construct a projection operator such that the drift coefficient, the memory kernel, and the fluctuating force of the generalized Langevin equation are the same as for the system without external driving. We show that next to the external force another force term occurs that is caused by the nonequilibrium response of the solvent. The first contribution to the ensemble average of this force stems from third or higher order terms of the external force and from sixth or higher order terms of time. We also analyze the additional force term numerically for an exemplary system. Published by the American Physical Society 2024

Resistance Drift in Melt-Quenched Ge2Sb2Te5 Phase Change Memory Line Cells at Cryogenic Temperatures

We characterized resistance drift in phase change memory devices in the 80 K to 300 K temperature range by performing measurements on 20 nm thick, ∼70–100 nm wide lateral Ge2Sb2Te5 (GST) line cells. The cells were amorphized using 1.5–2.5 V pulses with ∼50–100 ns duration leading to ∼0.4–1.1 mA peak reset currents resulting in amorphized lengths between ∼50 and 700 nm. Resistance drift coefficients in the amorphized cells are calculated using constant voltage measurements starting as fast as within a second after amorphization and for 1 h duration. Drift coefficients range between ∼0.02 and 0.1 with significant device-to-device variability and variations during the measurement period. At lower temperatures (higher resistance states) some devices show a complex dynamic behavior, with the resistance repeatedly increasing and decreasing significantly over periods in the order of seconds. These results point to charge trapping and de-trapping events as the cause of resistance drift.

Interactive Hybrid Model for Remaining Useful Life Prediction With Uncertainty Quantification of Bearing in Nuclear Circulating Water Pump

Journal bearings are the key components of the nuclear circulating water pump (NCWP), and accurate remaining useful life (RUL) prediction is of great significance for improving the reliability, safety, and maintenance planning of NCWP. However, it is difficult to quantify the uncertainty of bearing RUL based on the current deep learning (DL) model, resulting in a lack of credibility and effective convincing for RUL predicted by the model. Meanwhile, all existing hybrid models are basically simple combinations, and they cannot solve the uncertainty quantification problem of RUL predicted by DL. Hence, the bearing RUL prediction method based on a dynamic interactive hybrid model is proposed. Firstly, a degradation model based on a nonlinear enhanced generalized Wiener process (EGWP) is proposed, which combines gated neural networks and time-varying drift coefficients to describe the nonlinear degradation process of bearing. Then, a corrective gated recurrent unit (CGRU) network is designed to learn and predict real-time degradation increments, and the parameters of the degradation model are dynamically updated through the history and prediction of degradation increments. Finally, the bearing RUL prediction is given by the CGRU network, and the probability density function (PDF) of RUL is given by the proposed hybrid model. The performance of the proposed method is evaluated using the PHM 2012 bearing dataset and the NCWP journal bearing dataset. The results show that our proposed method can effectively predict bearing RUL and its uncertainty.

Convergence rate of the Euler–Maruyama scheme applied to diffusion processes with Lq−Lρ drift coefficient and additive noise

Convergence rate of the Euler–Maruyama scheme applied to diffusion processes with Lq−Lρ drift coefficient and additive noise

Periodic self-triggered strategy for highly non-linear hybrid stochastic delayed networks based on impulsive control

This article investigates the stabilization issue of highly non-linear hybrid stochastic delayed networks (HSDNs) via periodic self-triggered control under impulse (PS-TCI). Firstly, the existence of a unique global solution for highly non-linear HSDNs under PS-TCI is studied. Then, a stabilization criterion for highly non-linear HSDNs is established, by combining a graph-theoretic approach with a novel Lyapunov-based analysis, based on a ‘genuine’ Lyapunov function defined by introducing an auxiliary timer. Therein, the less conservative polynomial growth condition and local Lipschitz condition for the drift and diffusion coefficients are used than the linear growth condition and global Lipschitz condition. Meanwhile, the design idea of PS-TCI is based on the evolution of an upper bound of the mathematical expectation for Lyapunov function (not directly Lyapunov function or system state), which implies that the triggered instant of PS-TCI is not a random variable. Finally the theoretical results are employed to study the stability of a class of FitzHugh–Nagumo circuits networks and the central pattern generators networks of a hexapod robot, and correlative numerical simulations are provided for demonstration.

One-dimensional SDEs with LPS-type singular drift coefficients and Hölder continuous diffusion coefficients

In this paper, under the assumptions of LPS-type singular drift coefficients and Hölder continuous diffusion coefficients, the existence, uniqueness, stability, non-confluent property and strong Feller property for the solution to a one-dimensional stochastic differential equations are obtained. Our proof are based on the tools of local time and Zvonkin's transform.

Optimal investment in ambiguous financial markets with learning

We consider the classical multi-asset Merton investment problem under drift uncertainty, i.e. the asset price dynamics are given by geometric Brownian motions with constant but unknown drift coefficients. The investor assumes a prior drift distribution and is able to learn by observing the asset prize realizations during the investment horizon. While the solution of an expected utility maximizing investor with constant relative risk aversion (CRRA) is well known, we consider the optimization problem under risk and ambiguity preferences by means of the KMM (Klibanoff et al., 2005) approach. Here, the investor maximizes a double certainty equivalent. The inner certainty equivalent is for given drift coefficient, the outer is based on a drift distribution. Assuming also a CRRA type ambiguity function, it turns out that the optimal strategy can be stated in terms of the solution without ambiguity preferences but an adjusted drift distribution. To the best of our knowledge an explicit solution method in this setting is new. We rely on some duality theorems to prove our statements.Based on our theoretical results, we are able to shed light on the impact of the prior drift distribution as well as the consequences of ambiguity preferences via the transfer to an adjusted drift distribution, i.e. we are able to explain the interaction of risk and ambiguity preferences. We compare our results with the ones in a pre-commitment setup where the investor is restricted to deterministic strategies. It turns out that (under risk and ambiguity aversion) an infinite investment horizon implies in both cases a maximin decision rule, i.e. the investor follows the worst (best) Merton fraction (over all realizations of it) if she is more (less) risk averse than a log-investor. We illustrate our findings with an extensive numerical study.

Tamed-adaptive Euler-Maruyama approximation for SDEs with superlinearly growing and piecewise continuous drift, superlinearly growing and locally Hölder continuous diffusion

In this paper, we consider stochastic differential equations whose drift coefficient is superlinearly growing and piecewise continuous, and whose diffusion coefficient is superlinearly growing and locally Hölder continuous. We first prove the existence and uniqueness of solution to such stochastic differential equations and then propose a tamed-adaptive Euler-Maruyama approximation scheme. We study the rate of convergence in L1-norm of the scheme in both finite and infinite time intervals.

A self-centering and stiffness-controlled MEMS accelerometer

This paper presents a high-performance MEMS accelerometer with a DC/AC electrostatic stiffness tuning capability based on double-sided parallel plates (DSPPs). DC and AC electrostatic tuning enable the adjustment of the effective stiffness and the calibration of the geometric offset of the proof mass, respectively. A dynamical model of the proposed accelerometer was developed considering both DC/AC electrostatic tuning and the temperature effect. Based on the dynamical model, a self-centering closed loop is proposed for pulling the reference position of the force-to-rebalance (FTR) to the geometric center of DSPP. The self-centering accelerometer operates at the optimal reference position by eliminating the temperature drift of the readout circuit and nulling the net electrostatic tuning forces. The stiffness closed-loop is also incorporated to prevent the pull-in instability of the tuned low-stiffness accelerometer under a dramatic temperature variation. Real-time adjustments of the reference position and the DC tuning voltage are utilized to compensate for the residue temperature drift of the proposed accelerometer. As a result, a novel controlling approach composed of a self-centering closed loop, stiffness-closed loop, and temperature drift compensation is achieved for the accelerometer, realizing a temperature drift coefficient (TDC) of approximately 7 μg/°C and an Allan bias instability of less than 1 μg.

Comparison of Statistical Approaches for Reconstructing Random Coefficients in the Problem of Stochastic Modeling of Air–Sea Heat Flux Increments

This paper compares two statistical methods for parameter reconstruction (random drift and diffusion coefficients of the Itô stochastic differential equation, SDE) in the problem of stochastic modeling of air–sea heat flux increment evolution. The first method relates to a nonparametric estimation of the transition probabilities (wherein consistency is proven). The second approach is a semiparametric reconstruction based on the approximation of the SDE solution (in terms of distributions) by finite normal mixtures using the maximum likelihood estimates of the unknown parameters. This approach does not require any additional assumptions for the coefficients, with the exception of those guaranteeing the existence of the solution to the SDE itself. It is demonstrated that the corresponding conditions hold for the analyzed data. The comparison is carried out on the simulated samples, modeling the case where the SDE random coefficients are represented in trigonometric form, which is related to common climatic models, as well as on the ERA5 reanalysis data of the sensible and latent heat fluxes in the North Atlantic for 1979–2022. It is shown that the results of these two methods are close to each other in a quantitative sense, but differ somewhat in temporal variability and spatial localization. The differences during the observed period are analyzed, and their geophysical interpretations are presented. The semiparametric approach seems promising for physics-informed machine learning models.

A 65 nm CMOS rail-to-rail auto-zero operational amplifier based on charge pump internal power supply

A high-gain, low-offset, and low-power auto-zero operational amplifier with rail-to-rail input/output is proposed. Based on a time-interleaved charge pump high-voltage on-chip internal power supply, the PMOS differential pair input configuration will achieve a rail-to-rail input range with constant transconductance. Time-interleaved auto-zero continuously eliminates the input offset voltage of the operational amplifier in the time domain. An nA-level bias circuit to realize low power. The operational amplifier circuit is based on a 65 nm CMOS process. Under 1.2V power supply voltage and temperature 27 °C, the input offset voltage of the operational amplifier is 3.16 μV and the input offset current is less than 20 pA. The temperature drift coefficient of offset voltage is 0.005 μV/°C between −40 °C and 90 °C. The variation rate of input transconductance is only 5.6 % among the rail-to-rail input range. The equivalent DC gain is 106.4 dB, the unit gain bandwidth is 0.54 MHz, the phase margin is 76.5°, and the power consumption is about 0.19 mW. The layout area is 0.83 × 0.75 mm2.