Keywords: 60H10; 65C30; SDEs with time-dependent delay; Non explosion; MTEM method; Almost sure polynomial stability; Mean square polynomial stability;
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Keywords: 60H15; 60H35; 65C30; Stochastic heat equation; Fractional noise; Bismut formula; Harnack inequality;
Keywords: Stochastic age-dependent capital system; Mean-square dissipativity; Numerical methods; Fractional Brownian motion; Poisson jumps; 60H10; 60H05; 60H35; 65C30;
Keywords: 37H10; 39A50; 60H35; 65C30; Adaptive timestepping; Euler-Maruyama method; Locally Lipschitz coefficients; A.s. stability and instability; Positivity;
Keywords: 60H10; 65C30; 65L20; Stochastic differential equations; Local Lipschitz condition; Modified truncated Euler-Maruyama method; Strong convergence rate;
Keywords: 60H10; 60H35; 65C20; 65C30; 65J15; 65L20; 92D99; Explicit numerical scheme; Semi-discrete method; Non-linear SDEs; Strong approximation error; Boundary preserving numerical algorithm; Wright-Fisher model;
Keywords: 60H35; 60H30; 60H10; 65C30; Jump-diffusion; Numerical solution; Balanced implicit method; Positivity preserving;
Keywords: 65C30; Stochastic functional differential equation; Polynomial growth condition; Backward Euler-Maruyama method; Strong convergence; Boundedness;
Keywords: primary; 65C30; 60H10; Stochastic differential equation; Euler-Maruyama scheme; Discontinuous drift; Weak rate of convergence; Malliavin calculus;
Keywords: 65C30; 60H15; 60H35Navier–Stokes equations; Oseen–Stokes equations; Helmholtz–Hodge–Leray decomposition; Stochastic partial differential equations; Conditional Feynman–Kac formula; Weak approximation of stochastic differential equations and layer methods
Keywords: Waveform relaxation methods; Superlinear convergence; Stochastic differential equations; Neutral stochastic functional differential equations; Mean square convergence; 34K50; 60H35; 65C30;
Keywords: Stochastic age-dependent population equations; Numerical solution; Positivity preserving; Convergence60H35; 60H30; 60H10; 65C30
Keywords: 26A33; 65C30; 47H10; 93B05Stochastic differential equations of Sobolev-type; Existence and uniqueness; Fractional derivatives; Non-Lipschitz coefficients
Keywords: 60H15; 60H35; 65C05; 65C30; 60H10Burgers equation; Boundary Neumann noise; Galerkin method; Weak approximation; Exponential Euler scheme; Impact of noise
Almost sure convergence rate of θ-EM scheme for neutral SDDEs
Keywords: 65C30; 65L20; Neutral stochastic differential delay equations; θ-EM scheme; Local Lipschitz; Almost sure convergence; Strong convergence;
Asymptotic exponential stability of modified truncated EM method for neutral stochastic differential delay equations
Keywords: 65C30; 65L20; Neutral stochastic differential delay equations; Modified truncated Euler-Maruyama method; Mean-square exponential stability; Almost sure exponential stability;
Wavelet Galerkin method for fourth order linear and nonlinear differential equations
Keywords: Daubechies wavelet; 2-term connection coefficients; Periodic scaling function; Multiresolution analysis; Wavelet Galerkin method; 65T60; 65C30; 31A30;
Convergence and non-negativity preserving of the solution of balanced method for the delay CIR model with jump
Keywords: primary; 60H10; 60H35; secondary; 65c30; Stochastic delay differential equation (SDDE) with jump; The delay CIR model with jump; Balanced method; Convergence; Non-negativity; Moment boundedness;
Euler polynomial solutions of nonlinear stochastic Itô-Volterra integral equations
Keywords: 65C30; 60H35; 60H20; Stochastic Itô-Volterra integral equations; Brownian motion process; Stochastic operational matrix; Euler polynomials; Error analysis;
Strong convergence of a tamed theta scheme for NSDDEs with one-sided Lipschitz drift
Keywords: Tamed theta scheme; Neutral stochastic differential delay equations; One-sided Lipschitz; Strong convergence; 65C30; 65L20;
Finite element methods and their error analysis for SPDEs driven by Gaussian and non-Gaussian noises
Keywords: Stochastic partial differential equations; Gaussian and non-Gaussian noises; Finite element method; Linear implicit Euler scheme; Regularity; Mean square error; 60H15; 60H35; 65C30; 65M60;
Convergence of numerical solutions to stochastic differential equations with Markovian switching
Keywords: Stochastic differential equations; Markovian switching; Generalized Itô formula; Simulation; Numerical approximations; 60H35; 34K50; 65C30;
Application of orthonormal Bernstein polynomials to construct a efficient scheme for solving fractional stochastic integro-differential equation
Keywords: 26A33; 65C30; 33C45; 65D30; Fractional calculus; Stochastic integral equation; Operational matrix; Orthonormal polynomials; Error analysis;
Application of operational matrices for solving system of linear Stratonovich Volterra integral equation
Keywords: 65C30; 60H20; 60H35; 60J65; Linear Stratonovich Volterra integral equations; Stochastic operational matrix; Computational methods for stochastic equations; Brownian motion process; Block pulse functions; Error analysis;
Optimal pointwise approximation of SDE's from inexact information
Keywords: 68Q25; 65C30; Noisy information; Pointwise approximation; Deterministic noise; Optimal approximation; Minimal error; Monte Carlo algorithms;
A weak Local Linearization scheme for stochastic differential equations with multiplicative noise
Keywords: 65C30; 60H10; 60H35; Stochastic differential equation; Mean-square stability; Weak convergence; Local Linearization scheme;
Strong rate of convergence for the Euler-Maruyama approximation of SDEs with Hölder continuous drift coefficient
Keywords: 60H35; 41A25; 60H10; 65C30; Euler-Maruyama approximation; Strong approximation; Rate of convergence; Hölder continuous drift; Truncated symmetric α-stable;
Adaptive importance sampling in least-squares Monte Carlo algorithms for backward stochastic differential equations
Keywords: 49L20; 60H07; 62Jxx; 65C30; 93E24; Backward stochastic differential equations; Empirical regressions; Importance sampling;
Approximation solution of nonlinear Stratonovich Volterra integral equations by applying modification of hat functions
Keywords: 65C30; 65C20; 60H20; 60H35; 68U20Modification of hat functions; Nonlinear Stratonovich Volterra integral equation; Hyers–Ulam–Rassias stability; Operational matrix; Error analysis
Multi-step methods for random ODEs driven by Itô diffusions
Keywords: 34F05; 65C30; 60H25; 65L45; 65N40Random ODE and PDE; Itô diffusion; Pathwise convergence; Linear multi-step methods; B-stability; Method of lines
Asymptotic mean-square stability of explicit Runge–Kutta Maruyama methods for stochastic delay differential equations
Keywords: 60H10; 65C30; 65L03; 65L20Explicit method; Runge–Kutta; Stochastic delay differential system; Mean-square stability; Stabilized method
Efficient numerical Fourier methods for coupled forward–backward SDEs
Keywords: 91G60; 60H35; 65C30; 65T50; 60E10; 65B05Fourier-cosine expansion method; Characteristic function; Coupled forward–backward stochastic differential equations; Richardson extrapolation; Second-order convergence; Cross-hedging
A high-order discontinuous Galerkin method for Itô stochastic ordinary differential equations
Keywords: 60H10; 60H35; 65C20; 65C30; 65L20; 65L60Itô stochastic differential equation; Discontinuous Galerkin method; Wong–Zakai approximation; A-stability; Mean-square convergence; Order of convergence
Minimal asymptotic error for one-point approximation of SDEs with time-irregular coefficients
Keywords: 68Q25; 65C30; Non-standard assumptions; One-point approximation; Lower bounds; Asymptotic error; Optimal algorithm; Monte Carlo methods;
Optimal global approximation of SDEs with time-irregular coefficients in asymptotic setting
Keywords: Non-standard assumptions; Global approximation; Adaptive/nonadaptive standard information; Minimal error algorithm; Monte Carlo algorithms; 68Q25; 65C30;
Convergence and convergence rates for approximating ergodic means of functions of solutions to stochastic differential equations with Markov switching
Keywords: 60H35; 60J60; 65C30; Switching diffusion; Recursive algorithm; Invariant measure; Law of iterated logarithm;
A multi-step Richardson-Romberg extrapolation method for stochastic approximation
Keywords: 60H35; 65C30; 65C05; Euler scheme; Weak error; Richardson-Romberg extrapolation; Stochastic approximation algorithm;
Efficient almost-exact Lévy area sampling
Keywords: 60H05; 60H35; 65C30; 91G60Lévy area; Strong simulation; Logistic expansion; Chebyshev approximation; Milstein method
A note on sufficient conditions for asymptotic stability in distribution of stochastic differential equations with Markovian switching
Keywords: 34K50; 34K20; 65C30; 60J10Stochastic differential equations; Stability in distribution; Itô’s formula; Markovian switching
Strong order one convergence of a drift implicit Euler scheme: Application to the CIR process
Keywords: 65C30; 60H35Drift implicit Euler scheme; Cox–Ingersoll–Ross model; Strong error; Lamperti transformation
Strong convergence and stability of implicit numerical methods for stochastic differential equations with non-globally Lipschitz continuous coefficients
Keywords: 65C30; 65L20; 60H10Super-linear growth; Stochastic differential equation; Strong convergence; Backward Euler–Maruyama scheme; LaSalle principle; Almost sure stability
A derivative-free explicit method with order 1.0 for solving stochastic delay differential equations
Keywords: 65C30; 60H35Explicit order 1.0 strong scheme; Stochastic delay differential equations; Mean-square stability; Numerical experiments
A mean-reverting SDE on correlation matrices
Keywords: 65C30; 60H35; 91B70; Correlation; Wright-Fisher diffusions; Multi-allele Wright-Fisher model; Jacobi processes; Wishart processes; Discretization schemes; Multi-asset model;
Application of the Polynomial Chaos Expansion to the simulation of chemical reactors with uncertainties
Keywords: 41A10; 60Gxx; 65C30; 92E20Polynomial chaos; Stochastic differential equations; Chemical kinetics; Nitric oxide reduction
Existence, minimality and approximation of solutions to BSDEs with convex drivers
Keywords: 60H10; 65C30; Backward stochastic differential equations; Backward stochastic difference equations; Convex drivers; Discrete-time approximations; Supersolutions;
Convergence of numerical solutions for a class of stochastic age-dependent capital system with Markovian switching
Keywords: 60H10; 60H05; 60H35; 65C30; Stochastic age-dependent capital system; Markovian switching; Numerical solution; Euler approximation;
Convergence rate of numerical solutions to SFDEs with jumps
Keywords: 65C30; 65L20; 60H35Euler–Maruyama; Local Lipschitz condition; SFDE; Convergence rate; Poisson process
Runge-Kutta methods for jump-diffusion differential equations
Keywords: 60H35; 60H10; 65C30; 60J75; 65L06; Runge-Kutta methods; Jump-diffusion; Small noise; Mean-square convergence;
Concentration effects in mesoscopic simulation of coarsening
Keywords: 65C30; 68U20; 82C80Lifshitz–Slyozov growth law; Stochastic partial differential equations; Spectral methods; Mesoscopic models; Monte Carlo simulation
A Lax equivalence theorem for stochastic differential equations
Keywords: 60G60; 60H15; 60H35; 65C30; 65C05Stochastic partial differential equations; Lax equivalence theorem; Numerical approximation; Consistency; Stability; Convergence