Application of stochastic phenomenological modelling to cell−to−cell and beat−to−beat electrophysiological variability in cardiac tissue by Walmsley, J, Mirams, G, Pitt−Francis, J, Rodriguez, B, Burrage, K

“…We developed four cell-specific parameterizations of a phenomenological stochastic differential equation AP model exhibiting intrinsic variability using APs recorded from isolated guinea pig ventricular myocytes exhibiting BVR. …”

On Azéma-Yor processes, their optimal properties and the Bachelier-drawdown equation by Carraro, L, Karoui, N, Obloj, J

“…We show that they arise as unique strong solutions of the Bachelier stochastic differential equation which we prove is equivalent to the drawdown equation. …”

Stochastic approach to a rain attenuation time series synthesizer for heavy rain regions by Masoud, Mohebbi Nia, Din, Jafri, Lam, Hong Yin, Athanosios, D. Panagopoulos

“…The model combines a well­known interestrate prediction model in finance namely the Cox­Ingersoll­Ross (CIR) model, and a stochastic differential equation approach to generate a longterm gamma distributed rain attenuation time series, particularly appropriate for heavy rain regions. …”

Divergent Resistance Mechanisms to Immunotherapy Explain Responses in Different Skin Cancers by Emmanuel Dollinger, Daniel Bergman, Peijie Zhou, Scott X. Atwood, Qing Nie

“…We further explored the relationships between macrophages, B cells and response to checkpoint therapy by developing a stochastic differential equation model which qualitatively agrees with the data analysis. …”
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Spurious Memory in Non-Equilibrium Stochastic Models of Imitative Behavior by Vygintas Gontis, Aleksejus Kononovicius

“…A good example of Markov processes with spurious memory is a stochastic process driven by a non-linear stochastic differential equation (SDE). This example is at odds with models built using fractional Brownian motion (fBm). …”
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Closed-Form Formula for the Conditional Moments of Log Prices under the Inhomogeneous Heston Model by Kittisak Chumpong, Patcharee Sumritnorrapong

“…Several financial instruments have been thoroughly calculated via the price of an underlying asset, which can be regarded as a solution of a stochastic differential equation (SDE), for example the moment swap and its exotic types that encourage investors in markets to trade volatility on payoff and are especially beneficial for hedging on volatility risk. …”
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Multi-assets Asian rainbow options pricing with stochastic interest rates obeying the Vasicek model by Yao Fu, Sisi Zhou, Xin Li, Feng Rao

“…By introducing the Vasicek model as the change process of the stochastic interest rate, based on the non-arbitrage principle and the stochastic differential equation, the number of assets of the Asian rainbow option is expanded to n dimensions, and the pricing formulas of the Asian rainbow option with multiple (n) assets under the Vasicek interest rate model are obtained. …”
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Catalyst: Fast and flexible modeling of reaction networks. by Torkel E Loman, Yingbo Ma, Vasily Ilin, Shashi Gowda, Niklas Korsbo, Nikhil Yewale, Chris Rackauckas, Samuel A Isaacson

“…Catalyst supports simulating stochastic chemical kinetics (jump process), chemical Langevin equation (stochastic differential equation), and reaction rate equation (ordinary differential equation) representations for CRNs. …”
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Malliavin Calculus and Its Application to Robust Optimal Investment for an Insider by Chao Yu, Yuhan Cheng

“…When the insider is ’large’, we articulate a quadratic backward stochastic differential equation characterization of the investment. …”
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An extension of the stochastic sewing lemma and applications to fractional stochastic calculus by Toyomu Matsuda, Nicolas Perkowski

“…The third is to improve a regularity assumption on the diffusion coefficient of a stochastic differential equation driven by a fractional Brownian motion for pathwise uniqueness and strong existence.…”
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Numerical solution of the modified and non-Newtonian Burgers equations by stochastic coded trees by Nguwi, Jiang Yu, Privault, Nicolas

“…Our implementation uses neural networks that yield a functional space-time domain estimation, and includes numerical comparisons with the deep Galerkin (DGM) and deep backward stochastic differential equation (BSDE) methods.…”
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Probability distribution of returns in Heston model for index prices of FTSE Bursa Malaysia KLCI by Tey, Seah Ying

“…The solutions of the stochastic differential equation were approximated by Euler-Maruyama method. …”
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Can Short and Partial Observations Reduce Model Error and Facilitate Machine Learning Prediction? by Nan Chen

“…For a rich class of nonlinear and non-Gaussian systems, the conditional sampling is carried out by solving a simple stochastic differential equation, which is computationally efficient and accurate. …”
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Probabilistic Analysis of the Auto Tracking Failure by the Mobile Robot Video System by A. A. Lobaty, M. M. Tatur, A. K. Ibrahim

“…The mathematical formulation of the probabilistic analysis problem is based on the processes representation occurring in the system by a vector stochastic differential equation. The condition for the auto tracking failure is the exit of the tracked object from the of the video system field of view and non-return to it within a specified time. …”
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Influence of initial heeling angle on ship roll motion response by Zewen ZHANG, Xiangya LOU, Xiangpeng YU, Lin HE, Wei CHAI

“…MethodsSpecifically, the path integration method is applied to solve the Fokker-Planck equation, which governs the probability properties of the stochastic differential equation for the roll motion. The probability distributions of the roll motion response can then be obtained. …”
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A stochastic model of preventive maintenance strategies for wind turbine gearboxes considering the incomplete maintenance by Hongsheng Su, Yuqi Li, Qian Cao

“…Therefore, this paper takes the gearbox as a case study to introduce the incomplete maintenance parameters into the failure rate function to establish a state model based on the stochastic differential equation (SDE) and describing the state change of incomplete maintenance. …”
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A stochastic model with jumps for smoking incorporating media coverage by Mohamed COULIBALY, Modeste N'Zi

“…We prove that the solution of the stochastic differential equation with jumps of the stochastic model is unique, positive and global. …”
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Theoretical and Numerical Study of Self-Organizing Processes in a Closed System Classical Oscillator and Random Environment by Ashot S. Gevorkyan, Aleksander V. Bogdanov, Vladimir V. Mareev, Koryun A. Movsesyan

“…A self-organizing joint system classical oscillator–random environment is considered within the framework of a complex probabilistic process that satisfies a Langevin-type stochastic differential equation. Various types of randomness generated by the environment are considered. …”
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Stochastic Resonance Observed in Aerosol Optical Depth Time Series by Mariarosaria Falanga, Enza De Lauro, Salvatore de Martino

“…This means that a simple, although stochastic, differential equation can represent the time evolution of the optical depth, at least concerning its component related to the annual cycle.…”
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Trivariate Stochastic Weather Model for Predicting Maize Yield by Patrick Chidzalo, Phillip O. Ngare, Joseph K. Mung’atu

“…Stochastic analyses are applied on the pdf and process to account for nonlinearity and nonstationarity, and also establish a corresponding stochastic differential equation (SDE) for maize yield. The trivariate stochastic process predicts maize yield with R2=0.8389 and MAPE=4.31% under a deep learning framework. …”
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