Multilevel path branching for digital options by Giles, MB, Haji-Ali, A-L

“…We propose a new Monte Carlo-based estimator for digital options with assets modelled by a stochastic differential equation (SDE). The new estimator is based on repeated path splitting and relies on the correlation of approximate paths of the underlying SDE that share parts of a Brownian path. …”

Learning to track the visual motion of contours by Blake, A, Isard, M, Reynard, D

“…The image sequence is used to learn parameters in a stochastic differential equation model. These are used, in turn, to build a tracker whose predictor imitates the motion in the training set. …”

Existence of solutions to a class of indefinite stochastic Riccati equations by Qian, Z, Zhou, X

“…An indefinite stochastic Riccati equation is a matrix-valued, highly nonlinear backward stochastic differential equation together with an algebraic, matrix positive definiteness constraint. …”

A framework for ship stability in a seastate using the state-space Fokker-Planck method by Larson, David F. H

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TENTANG ASPEK STOKASTIK DIFUSI PADA KERAGAMAN BERBOBOT by , NURFARISHA, , Dr.rer.nat. M. Farchani Rosyid

“…Stochastic process extention has been built for a diffusion on weighted manifolds through stochastic differential equation. Diffusion process extention is done by reformulating weighted Laplasian-Beltrami operator which is functioned as a generator in that process. …”

An FBSDE approach to the Skorokhod embedding problem for Gaussian processes with non-linear drift by Fromm, A, Imkeller, P, Prömel, D

“…Our approach relies on solving an associated strongly coupled system of Forward Backward Stochastic Differential Equation (FBSDE), and investigating the regularity of the obtained solution. …”

Towards a further understanding of the dynamics in the excitatory NNLIF neuron model: blow-up and global existence by Roux, P, Salort, D

“…The Nonlinear Noisy Leaky Integrate and Fire (NNLIF) model is widely used to describe the dynamics of neural networks after a diffusive approximation of the mean-field limit of a stochastic differential equation. In previous works, many qualitative results were obtained: global existence in the inhibitory case, finite-time blow-up in the excitatory case, convergence towards stationary states in the weak connectivity regime. …”

A model for a large investor trading at market indifference prices. II: Continuous-time case by Bank, P, Kramkov, D

“…As a result, we show that the model’s evolution can be described by a nonlinear stochastic differential equation for the market makers’ expected utilities. …”

Business cycle and herding behavior in stock returns: theory and evidence by Kwangwon Ahn, Linxiao Cong, Hanwool Jang, Daniel Sungyeon Kim

“…Starting with a conventional stochastic differential equation representing the evolution of stock returns, we provide a simple theoretical model and empirically demonstrate it. …”
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Controlled Reflected McKean–Vlasov SDEs and Neumann Problem for Backward SPDEs by Li Ma, Fangfang Sun, Xinfang Han

“…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. …”
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Identification of a Stochastic Dynamic Model for Aircraft Flight Attitude Based on Measured Data by Haiquan Li, Xiaoqian Chen, Jiatu Zhang, Bochen Wang, Jiahui Peng, Liang Wang

“…Therefore, a stochastic differential equation for aircraft flight attitude is modeled based on the traditional one in this paper. …”
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The stability of a stochastic discrete SIVS epidemic model with general nonlinear incidence by Buyu Wen, Zhidong Teng, Bing Liu

“… In this paper, based on Euler–Marryama method and theory of stochastic processes, a stochastic discrete SIVS epidemic model with general nonlinear incidence and vaccination is proposed by adding random perturbation and then discretizing the corresponding stochastic differential equation model. Firstly, the basic properties of continuous and discrete deterministic SIVS epidemic models are obtained. …”
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A Constrained Approach to Multiscale Stochastic Simulation of Chemically Reacting Systems by Cotter, S, Zygalakis, K, Kevrekidis, I, Erban, R

“…We then show how using the ensuing Stochastic Differential Equation (SDE) approximation, we can in turn approximate average switching times in stochastic chemical systems.…”

Models for indices by Yee, Z

“…By taking the limit of a simple systems of stochastic differential equations (SDEs), we obtain a limit stochastic differential equation (SDE) for the index price. …”

Multilevel Monte Carlo for reliability theory by Aslett, L, Nagapetyan, T, Vollmer, S

“…In this paper we demonstrate how Multilevel Monte Carlo (MLMC) — a simulation approach which is typically used for stochastic differential equation models — can be applied in reliability problems by carefully controlling the bias-variance tradeoff in approximating large system behaviour. …”

Analysing multi-level Monte Carlo for options with non-globally Lipschitz payoff by Giles, M, Higham, D, Mao, X

“…Res. 56:607-617, 2008) introduced a multi-level Monte Carlo method for approximating the expected value of a function of a stochastic differential equation solution. A key application is to compute the expected payoff of a financial option. …”

Necessary optimality conditions of the second oder in a stochastic optimal control problem with delay argument by Rashad oglu Mastaliyev

“…The optimal control problem of nonlinear stochastic systems which mathematical model is given by Ito stochastic differential equation with delay argument is considered. …”
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Semiclassical phase reduction theory for quantum synchronization by Yuzuru Kato, Naoki Yamamoto, Hiroya Nakao

“…The dynamics of quantum dissipative systems exhibiting limit-cycle oscillations are reduced to a simple, one-dimensional classical stochastic differential equation approximately describing the phase dynamics of the system under the semiclassical approximation. …”
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Modeling the Effects of Chemotherapeutic Dose Response on a Stochastic Tumor-Immune Model of Prostate Cancer with Androgen Deprivation Therapy by Lin Chen, Jin Yang

“…In addition to analyzing the basic properties of solutions such as the tumor-free periodic solution and global attraction of the model, the threshold conditions for the persistence and extinction of prostate cancer cells and effector cells are obtained by using stochastic differential equation theory. Besides, sufficient conditions for the existence of stationary distribution of the system are established. …”
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Option valuation in markets with finite liquidity under fractional CEV assets by Azadeh Ghasemifard, Seddigheh Banihashemi, Afshin Babaei

“…Asset evolution satisfies a stochastic differential equation with fractional noise‎, ‎which is more realistic in markets with statistical dependence‎. ‎…”
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