Modelling the cervical cancer growth process by stochastic delay differential equations by Mazlan,, M. S. A., Rosli, N., Azmi, N. S., Bahar, A.

“…The growth process under Gompertz's law is considered, thus lead to stochastic differential equations of Gompertzian with time delay. …”
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Stochastic Modeling of Plant Virus Propagation with Biological Control by Benito Chen-Charpentier

“…Since there are always variations in the populations, errors in the measured values and uncertainties, we use two methods to introduce randomness: stochastic differential equations and the Gillespie algorithm. …”
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Higher-order numerical methods for stochastic simulation of chemical reaction systems by Székely Jr., T, Burrage, K, Erban, R, Zygalakis, K

“…This approach, as in the case of ordinary and stochastic differential equations, can be repeated to obtain even higher-order approximations. …”

Mean-square stability and error analysis of implicit time-stepping schemes for linear parabolic SPDEs with multiplicative Wiener noise in the first derivative by Reisinger, C

“…In this article, we extend a Milstein finite difference scheme introduced in 8 for a certain linear stochastic partial differential equation (SPDE) to semi-implicit and fully implicit time-stepping as introduced by Szpruch 32 for stochastic differential equations (SDEs). We combine standard finite difference Fourier analysis for partial differential equations with the linear stability analysis in 3 for SDEs to analyse the stability and accuracy. …”

Canonical RDEs and general semimartingales as rough paths by Chevyrev, I, Friz, P

“…In the spirit of Marcus canonical stochastic differential equations, we study a similar notion of rough differential equations (RDEs), notably dropping the assumption of continuity prevalent in the rough path literature. …”

A generalized Neyman-Pearson lemma for g-probabilities by Ji, S, Zhou, X

“…The problem is shown to be a special case of a general stochastic optimization problem where the objective is to choose the terminal state of certain backward stochastic differential equations so as to minimize a g-expectation. …”

Time-inconsistent stochastic linear-quadratic control: characterization and uniqueness of equilibrium by Hu, Y, Jin, H, Zhou, X

“…We derive a necessary and sufficient condition for equilibrium controls via a flow of forward–backward stochastic differential equations. When the state is one dimensional and the coefficients in the problem are all deterministic, we prove that the explicit equilibrium control constructed in [9] is indeed unique. …”

Time-Inconsistent Stochastic Linear--Quadratic Control by Hu, Y, Jin, H, Zhou, X

“…We define an equilibrium, instead of optimal, solution within the class of open-loop controls, and derive a sufficient condition for equilibrium controls via a flow of forward--backward stochastic differential equations. When the state is one dimensional and the coefficients in the problem are all deterministic, we find an explicit equilibrium control. …”

A more accurate numerical scheme for diffusive shock acceleration by Achterberg, A, Schure, K

“…We present a more accurate numerical scheme for the calculation of diffusive shock acceleration of cosmic rays using stochastic differential equations. The accuracy of this scheme is demonstrated using a simple analytical flow profile that contains a shock of finite width and a varying diffusivity of the cosmic rays, where the diffusivity decreases across the shock. …”

Time-Inconsistent Stochastic Linear--Quadratic Control by Hu, Y, Jin, H, Zhou, X

“…We define an equilibrium, instead of optimal, solution within the class of open-loop controls, and derive a sufficient condition for equilibrium controls via a flow of forward--backward stochastic differential equations. When the state is one dimensional and the coefficients in the problem are all deterministic, we find an explicit equilibrium control. …”

An adaptive Euler–Maruyama scheme for McKean–Vlasov SDEs with super-linear growth and application to the mean-field FitzHugh–Nagumo model by Reisinger, C, Stockinger, W

“…In this paper, we introduce fully implementable, adaptive Euler–Maruyama schemes for McKean–Vlasov stochastic differential equations (SDEs) assuming only a standard monotonicity condition on the drift and diffusion coefficients but no global Lipschitz continuity in the state variable for either, while global Lipschitz continuity is required for the measure component. …”

A path signature approach for speech emotion recognition by Wang, B, Liakata, M, Ni, H, Lyons, T, Nevado-Holgado, AJ, Saunders, K

“…Motivated by the numerical approximation theory of stochastic differential equations (SDEs), we propose the novel use of path signatures. …”

Two Approaches for a Dividend Maximization Problem under an Ornstein-Uhlenbeck Interest Rate by Julia Eisenberg, Stefan Kremsner, Alexander Steinicke

“…The properties and behavior of these optimal control problems in both settings are analyzed in an analytical HJB-driven approach, and we also use backward stochastic differential equations.…”
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Multi-shockpeakons for the stochastic Degasperis-Procesi equation by Lynnyngs K. Arruda

“…We prove that a stochastic perturbation of the Degasperis-Procesi equation also has weak multi-shockpeakon solutions if and only if the positions, momenta and shock strengths obey a system of $ 3n $ stochastic differential equations.…”
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Anticipating regime shifts by mixing early warning signals from different nodes by Naoki Masuda, Kazuyuki Aihara, Neil G. MacLaren

“…Based on theory of stochastic differential equations, we propose a method to optimize the node set from which to construct an early warning signal. …”
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Response of a three-species cyclic ecosystem to a short-lived elevation of death rate by Sourin Chatterjee, Rina De, Chittaranjan Hens, Syamal K. Dana, Tomasz Kapitaniak, Sirshendu Bhattacharyya

“…Numerical simulations using stochastic differential equations of the species give consistency to our results.…”
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Positive Solutions of the Fractional SDEs with Non-Lipschitz Diffusion Coefficient by Kęstutis Kubilius, Aidas Medžiūnas

“…We study a class of fractional stochastic differential equations (FSDEs) with coefficients that may not satisfy the linear growth condition and non-Lipschitz diffusion coefficient. …”
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Ellipsoidal Design of Robust Stabilization of Power Systems Exposed to a Cycle of Lightning Surges Modeled by Continuous-Time Markov Jumps by Alexander Poznyak, Hussain Alazki, Hisham M. Soliman, Razzaqul Ahshan

“…In this manuscript, the impact of the above stochastic disturbance on power system small-disturbance stability is studied based on stochastic differential equations (SDEs). The mean-square stabilization of such a system is conducted through a novel excitation control. …”
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Extinction and stationary distribution of stochastic predator-prey model with group defense behavior by Yansong Pei, Bing Liu, Haokun Qi

“…Some dynamical properties of the model, including the existence and uniqueness of global positive solution, sufficient conditions for extinction and unique ergodic stationary distribution, are investigated by using qualitative theory of stochastic differential equations, Lyapunov function analysis method, Itô formula, etc. …”
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Linear Stochastic Models in Discrete and Continuous Time by D. Stephen G. Pollock

“…The paper describes frequency-limited linear stochastic differential equations that conform to such a model, and it compares them with equations of a model that is assumed to be driven by a white-noise process of unbounded frequencies. …”
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