Advances in Difference Equations, ISSN 1687-1847, 12/2019, Volume 2019, Issue 1, pp. 1 - 15

This paper aims to examine and establish the models for European option pricing which include parameters of stochastic dividend yield and stochastic earning...

60H10 | Stochastic earning yield | Options pricing | Mathematics | Stochastic dividend yield | Black–Scholes–Merton model | Ordinary Differential Equations | Functional Analysis | Generalized Ornstein–Uhlenbeck process | 93E03 | Analysis | Difference and Functional Equations | Mathematics, general | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | Black-Scholes-Merton model | VALUATION | Generalized Ornstein-Uhlenbeck process | Performance evaluation | Economic models | Parameters | Computer simulation | Pricing | Mathematical models | Brownian movements | Options markets

60H10 | Stochastic earning yield | Options pricing | Mathematics | Stochastic dividend yield | Black–Scholes–Merton model | Ordinary Differential Equations | Functional Analysis | Generalized Ornstein–Uhlenbeck process | 93E03 | Analysis | Difference and Functional Equations | Mathematics, general | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | Black-Scholes-Merton model | VALUATION | Generalized Ornstein-Uhlenbeck process | Performance evaluation | Economic models | Parameters | Computer simulation | Pricing | Mathematical models | Brownian movements | Options markets

Journal Article

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Alternative way to derive the distribution of the multivariate Ornstein–Uhlenbeck process

Advances in Difference Equations, ISSN 1687-1847, 12/2019, Volume 2019, Issue 1, pp. 1 - 7

In this paper, we solve the Fokker–Planck equation of the multivariate Ornstein–Uhlenbeck process to obtain its probability density function. This approach...

60H10 | Multivariate normal distribution | Fokker–Planck equation | Multivariate Ornstein–Uhlenbeck process | Mathematics | Ordinary Differential Equations | Functional Analysis | 93E03 | Analysis | Difference and Functional Equations | Mathematics, general | n -dimensional Fourier transform | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | Fokker-Planck equation | n-dimensional Fourier transform | Multivariate Ornstein-Uhlenbeck process | Economic models | Statistical analysis | Covariance | Normal distribution | Covariance matrix | Multivariate analysis | Probability density functions

60H10 | Multivariate normal distribution | Fokker–Planck equation | Multivariate Ornstein–Uhlenbeck process | Mathematics | Ordinary Differential Equations | Functional Analysis | 93E03 | Analysis | Difference and Functional Equations | Mathematics, general | n -dimensional Fourier transform | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | Fokker-Planck equation | n-dimensional Fourier transform | Multivariate Ornstein-Uhlenbeck process | Economic models | Statistical analysis | Covariance | Normal distribution | Covariance matrix | Multivariate analysis | Probability density functions

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 11/2019, Volume 183, Issue 2, pp. 671 - 687

This paper investigates the necessary/sufficient conditions for Pareto optimality in the infinite horizon linear quadratic stochastic differential game. Based...

Stochastic differential game | Mathematics | Theory of Computation | Optimization | Generalized algebraic Riccati equation | 91A12 | 93E20 | Calculus of Variations and Optimal Control; Optimization | 93E03 | Operations Research/Decision Theory | Pareto optimality | Applications of Mathematics | Engineering, general | Infinite horizon | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SUFFICIENT CONDITIONS | OPTIMALITY | Pareto efficiency | Economic models | Pareto optimum | Maximum principle | Linear quadratic | Lagrange multiplier | Algebra | Stochastic systems | Lagrange multipliers | Optimal control | Horizon | Convexity | Riccati equation

Stochastic differential game | Mathematics | Theory of Computation | Optimization | Generalized algebraic Riccati equation | 91A12 | 93E20 | Calculus of Variations and Optimal Control; Optimization | 93E03 | Operations Research/Decision Theory | Pareto optimality | Applications of Mathematics | Engineering, general | Infinite horizon | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SUFFICIENT CONDITIONS | OPTIMALITY | Pareto efficiency | Economic models | Pareto optimum | Maximum principle | Linear quadratic | Lagrange multiplier | Algebra | Stochastic systems | Lagrange multipliers | Optimal control | Horizon | Convexity | Riccati equation

Journal Article

Computers & Industrial Engineering, ISSN 0360-8352, 10/2019, Volume 136, pp. 373 - 380

•Blockchain Governance Game as a unique security framework for the Blockchain network.•Security enhancement for the decentralized network.•Mathematical design...

Stochastic model | 60C55 | Blockchain | Bitcoin | Network security | 91A35 | 91A55 | 93C10 | Mixed game | 90B15 | 93E03 | Fluctuation theory | 90B50 | 51 percent attack | 60K10 | 93A30 | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, INDUSTRIAL

Stochastic model | 60C55 | Blockchain | Bitcoin | Network security | 91A35 | 91A55 | 93C10 | Mixed game | 90B15 | 93E03 | Fluctuation theory | 90B50 | 51 percent attack | 60K10 | 93A30 | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, INDUSTRIAL

Journal Article

Georgian Mathematical Journal, ISSN 1072-947X, 10/2017, Volume 26, Issue 3, pp. 423 - 436

We consider multivalued stochastic integral equations driven by semimartingales. Such equations are formulated in two different forms, i.e., using multivalued...

60H20 | 93E03 | 93C41 | 26E25 | EXISTENCE | MATHEMATICS | HUKUHARA DIFFERENTIABILITY | OPERATOR | SPACES | STABILITY | Multivalued stochastic integral equations | multivalued differential equations | multivalued mappings | DELAY | SET DIFFERENTIAL-EQUATIONS

60H20 | 93E03 | 93C41 | 26E25 | EXISTENCE | MATHEMATICS | HUKUHARA DIFFERENTIABILITY | OPERATOR | SPACES | STABILITY | Multivalued stochastic integral equations | multivalued differential equations | multivalued mappings | DELAY | SET DIFFERENTIAL-EQUATIONS

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 6/2019, Volume 16, Issue 3, pp. 1 - 14

In this paper, we deal with uncertainty quantification for the random Legendre differential equation, with input coefficient A and initial conditions $$X_0$$...

uncertainty quantification | 60H10 | 93E03 | Mathematics, general | Mathematics | random power series | random Legendre differential equation | 65C05 | mean square calculus | 65C60 | 34F05 | 60H35 | MATHEMATICS | MATHEMATICS, APPLIED | CONVERGENCE | GENERALIZED POLYNOMIAL CHAOS | Monte Carlo method | Analysis | Stochastic processes | Differential equations

uncertainty quantification | 60H10 | 93E03 | Mathematics, general | Mathematics | random power series | random Legendre differential equation | 65C05 | mean square calculus | 65C60 | 34F05 | 60H35 | MATHEMATICS | MATHEMATICS, APPLIED | CONVERGENCE | GENERALIZED POLYNOMIAL CHAOS | Monte Carlo method | Analysis | Stochastic processes | Differential equations

Journal Article

Journal of the London Mathematical Society, ISSN 0024-6107, 06/2019, Volume 99, Issue 3, pp. 609 - 628

We consider the Hamilton–Jacobi–Bellman system ∂tu−Δu=H(u,∇u)+ffor u∈RN, where the Hamiltonian H(u,∇u) satisfies a super‐quadratic growth condition with...

35K55 (primary) | 35B65 | 93E03 (secondary) | 91A06

35K55 (primary) | 35B65 | 93E03 (secondary) | 91A06

Journal Article

Journal of Mathematical Chemistry, ISSN 0259-9791, 5/2019, Volume 57, Issue 5, pp. 1314 - 1329

In this paper, we include simultaneously additive and multiplicative noise to the Pais–Uhlenbeck oscillator (PUO). We construct an integral of motion of the...

Additive noise | Theoretical and Computational Chemistry | Pais–Uhlenbeck oscillator | Chemistry | Multiplicative noise | Runge–Kutta method | 60H10 | Physical Chemistry | 93E03 | Integral of motion | 34F05 | Math. Applications in Chemistry | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | INVARIANTS | Pais-Uhlenbeck oscillator | SYSTEMS | Runge-Kutta method | CHEMISTRY, MULTIDISCIPLINARY | Hamiltonian systems | Usage | Learning models (Stochastic processes) | Models | Numerical analysis | Noise

Additive noise | Theoretical and Computational Chemistry | Pais–Uhlenbeck oscillator | Chemistry | Multiplicative noise | Runge–Kutta method | 60H10 | Physical Chemistry | 93E03 | Integral of motion | 34F05 | Math. Applications in Chemistry | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | INVARIANTS | Pais-Uhlenbeck oscillator | SYSTEMS | Runge-Kutta method | CHEMISTRY, MULTIDISCIPLINARY | Hamiltonian systems | Usage | Learning models (Stochastic processes) | Models | Numerical analysis | Noise

Journal Article

Stochastic Processes and their Applications, ISSN 0304-4149, 05/2019, Volume 129, Issue 5, pp. 1726 - 1748

This paper provides a new characterization of the stochastic invariance of a closed subset of Rd with respect to a diffusion. We extend the well-known inward...

Affine diffusions | Stochastic invariance | polynomial diffusions | Stochastic differential equation | DIFFUSIONS | VIABILITY | AFFINE PROCESSES | STATISTICS & PROBABILITY | Probability | Computational Finance | Mathematics | Quantitative Finance

Affine diffusions | Stochastic invariance | polynomial diffusions | Stochastic differential equation | DIFFUSIONS | VIABILITY | AFFINE PROCESSES | STATISTICS & PROBABILITY | Probability | Computational Finance | Mathematics | Quantitative Finance

Journal Article

Open Mathematics, ISSN 2391-5455, 12/2018, Volume 16, Issue 1, pp. 1651 - 1666

This paper presents a methodology to quantify computationally the uncertainty in a class of differential equations often met in Mathematical Physics, namely...

stochastic Galerkin projection technique | 93E03 | random Fröbenius method | computational uncertainty quantification | non-autonomous and random dynamical systems | 34F05 | adaptive generalized Polynomial Chaos | 60H35 | Stochastic Galerkin projection technique | Adaptive generalized Polynomial Chaos | Computational uncertainty quantification | Non-autonomous and random dynamical systems | Random Fröbenius method | MATHEMATICS | random Frobenius method | MODELS | GENERALIZED POLYNOMIAL CHAOS

stochastic Galerkin projection technique | 93E03 | random Fröbenius method | computational uncertainty quantification | non-autonomous and random dynamical systems | 34F05 | adaptive generalized Polynomial Chaos | 60H35 | Stochastic Galerkin projection technique | Adaptive generalized Polynomial Chaos | Computational uncertainty quantification | Non-autonomous and random dynamical systems | Random Fröbenius method | MATHEMATICS | random Frobenius method | MODELS | GENERALIZED POLYNOMIAL CHAOS

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 12/2018, Volume 15, Issue 6, pp. 1 - 19

The paper is devoted to the existence, uniqueness and asymptotic behaviors of mild solution to neutral impulsive stochastic integro-differential equations...

35B35 | 93E03 | resolvent operator | mild solution | existence | Mathematics, general | Mathematics | 60H15 | Fractional Brownian motion | neutral stochastic integro-differential equations | 39B82 | MATHEMATICS | MATHEMATICS, APPLIED | EVOLUTION-EQUATIONS | HILBERT-SPACE | DELAY | Differential equations

35B35 | 93E03 | resolvent operator | mild solution | existence | Mathematics, general | Mathematics | 60H15 | Fractional Brownian motion | neutral stochastic integro-differential equations | 39B82 | MATHEMATICS | MATHEMATICS, APPLIED | EVOLUTION-EQUATIONS | HILBERT-SPACE | DELAY | Differential equations

Journal Article

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Zero-Sum Discounted Reward Criterion Games for Piecewise Deterministic Markov Processes

Applied Mathematics & Optimization, ISSN 0095-4616, 12/2018, Volume 78, Issue 3, pp. 587 - 611

This papers deals with the zero-sum game with a discounted reward criterion for piecewise deterministic Markov process (PDMPs) in general Borel spaces. The two...

Secondary 91A05 | Systems Theory, Control | Continuous-time | Theoretical, Mathematical and Computational Physics | Mathematics | General borel spaces | Discounted reward criterion | Primary 90C40 | Mathematical Methods in Physics | Zero sum games | Calculus of Variations and Optimal Control; Optimization | 93E03 | 91A15 | Numerical and Computational Physics, Simulation | MATHEMATICS, APPLIED | TRANSITION-PROBABILITIES | Markov processes | Markov chains | Markov analysis | Criteria | Optimization and Control

Secondary 91A05 | Systems Theory, Control | Continuous-time | Theoretical, Mathematical and Computational Physics | Mathematics | General borel spaces | Discounted reward criterion | Primary 90C40 | Mathematical Methods in Physics | Zero sum games | Calculus of Variations and Optimal Control; Optimization | 93E03 | 91A15 | Numerical and Computational Physics, Simulation | MATHEMATICS, APPLIED | TRANSITION-PROBABILITIES | Markov processes | Markov chains | Markov analysis | Criteria | Optimization and Control

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2018, Volume 2018, Issue 1, pp. 1 - 29

In this paper we study random non-autonomous second order linear differential equations by taking advantage of the powerful theory of random difference...

60H10 | Mathematical modelling and stochastic computation | Random second order linear difference and differential equation | Uncertainty quantification | Mathematics | 37H10 | 34F05 | L p ( Ω ) $\mathrm {L}^{p}(\Omega)$ random calculus | Ordinary Differential Equations | Functional Analysis | 93E03 | Analysis | Difference and Functional Equations | Mathematics, general | 65C05 | Analytic second order stochastic process | Partial Differential Equations | 39A50 | 60H35 | (Ω) random calculus | MATHEMATICS | MATHEMATICS, APPLIED | CONVERGENCE | L-p(Omega) random calculus | Statistical analysis | Difference equations | Initial conditions | Computer simulation | Stochastic processes | Differential equations | Mathematical models | Stochastic models | Random variables

60H10 | Mathematical modelling and stochastic computation | Random second order linear difference and differential equation | Uncertainty quantification | Mathematics | 37H10 | 34F05 | L p ( Ω ) $\mathrm {L}^{p}(\Omega)$ random calculus | Ordinary Differential Equations | Functional Analysis | 93E03 | Analysis | Difference and Functional Equations | Mathematics, general | 65C05 | Analytic second order stochastic process | Partial Differential Equations | 39A50 | 60H35 | (Ω) random calculus | MATHEMATICS | MATHEMATICS, APPLIED | CONVERGENCE | L-p(Omega) random calculus | Statistical analysis | Difference equations | Initial conditions | Computer simulation | Stochastic processes | Differential equations | Mathematical models | Stochastic models | Random variables

Journal Article

11/2018

Proceedings of the Royal Society, A, Vol. 475, 2019 Determining evolution equations governing the probability density function (pdf) of non-Markovian responses...

Journal Article

Stochastic Analysis and Applications, ISSN 0736-2994, 11/2018, Volume 36, Issue 5, pp. 812 - 831

This contribution deals with the study of the almost sure exponential stability of large-scale stochastic systems with multiplicative noises. Under a...

Itô process | Multiplicative noises | 93E15 | Almost sure exponential stability | 93E03 | Large-scale stochastic system | LINEAR-SYSTEMS | MATHEMATICS, APPLIED | DESIGN | STABILIZATION | DIFFERENTIAL-EQUATIONS | STATE | STATISTICS & PROBABILITY | MEAN-SQUARE | Ito process | SEPARATION PRINCIPLE | PTH MOMENT | OBSERVER | STABILIZABILITY | Control systems | Stability | Stochastic systems | Nonlinear systems | Subsystems | Engineering Sciences | Automatic

Itô process | Multiplicative noises | 93E15 | Almost sure exponential stability | 93E03 | Large-scale stochastic system | LINEAR-SYSTEMS | MATHEMATICS, APPLIED | DESIGN | STABILIZATION | DIFFERENTIAL-EQUATIONS | STATE | STATISTICS & PROBABILITY | MEAN-SQUARE | Ito process | SEPARATION PRINCIPLE | PTH MOMENT | OBSERVER | STABILIZABILITY | Control systems | Stability | Stochastic systems | Nonlinear systems | Subsystems | Engineering Sciences | Automatic

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 8/2018, Volume 15, Issue 4, pp. 1 - 14

The invariance of a closed convex set K for weak solutions of stochastic functional differential equation is studied. Some necessary and sufficient conditions...

oriented distance | weak solution | 60H10 | stochastic functional differential equation | 93E03 | Mathematics, general | Mathematics | Stochastic invariance | MATHEMATICS | MATHEMATICS, APPLIED | VIABILITY | CONTROLLED DEGENERATE DIFFUSIONS | Differential equations

oriented distance | weak solution | 60H10 | stochastic functional differential equation | 93E03 | Mathematics, general | Mathematics | Stochastic invariance | MATHEMATICS | MATHEMATICS, APPLIED | VIABILITY | CONTROLLED DEGENERATE DIFFUSIONS | Differential equations

Journal Article

Journal of Difference Equations and Applications, ISSN 1023-6198, 05/2018, Volume 24, Issue 5, pp. 656 - 666

We discuss Conley-type approach to attractive sets for lower semicontinuous multifunctions. Since every iterated function system induces a Barnsley-Hutchinson...

iterated function system | lower semicontinuous multifunction | Primary: 28A80 | 54H20 | Conley attractor | 93E03 | limit set | Secondary: 26E25 | 47H04 | MATHEMATICS, APPLIED | SPACES | CLOSED RELATIONS | omega-limit set | CHAIN RECURRENCE | Applied mathematics | Topology

iterated function system | lower semicontinuous multifunction | Primary: 28A80 | 54H20 | Conley attractor | 93E03 | limit set | Secondary: 26E25 | 47H04 | MATHEMATICS, APPLIED | SPACES | CLOSED RELATIONS | omega-limit set | CHAIN RECURRENCE | Applied mathematics | Topology

Journal Article

International Journal of Systems Science, ISSN 0020-7721, 04/2018, Volume 49, Issue 6, pp. 1164 - 1177

In this paper, the problems on the pth moment and the almost sure exponential stability for a class of impulsive neutral stochastic functional differential...

impulsive | 60H10 | 93E03 | stochastic functional differential equations | Wiener process | neutral | exponential stability | Markovian switching | CRITERIA | MEAN-SQUARE | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | RAZUMIKHIN-TYPE THEOREMS | SYSTEMS | DELAY EQUATIONS | COMPUTER SCIENCE, THEORY & METHODS | ASYMPTOTIC STABILITY | SLIDING-MODE CONTROL | AUTOMATION & CONTROL SYSTEMS | Damping | Liapunov functions | Mathematical analysis | Tension tests | Differential equations | Markov processes | Stability analysis | Switching

impulsive | 60H10 | 93E03 | stochastic functional differential equations | Wiener process | neutral | exponential stability | Markovian switching | CRITERIA | MEAN-SQUARE | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | RAZUMIKHIN-TYPE THEOREMS | SYSTEMS | DELAY EQUATIONS | COMPUTER SCIENCE, THEORY & METHODS | ASYMPTOTIC STABILITY | SLIDING-MODE CONTROL | AUTOMATION & CONTROL SYSTEMS | Damping | Liapunov functions | Mathematical analysis | Tension tests | Differential equations | Markov processes | Stability analysis | Switching

Journal Article

Differential Equations and Dynamical Systems, ISSN 0971-3514, 1/2018, Volume 26, Issue 1, pp. 15 - 36

In this paper, we investigate the existence of mild solutions and the approximate controllability of a class of nonlinear fractional stochastic differential...

34K50 | Approximate controllability | Fixed point theorem | Fractional stochastic differential systems | 93E03 | 93B05 | Poisson jumps | Mathematics, general | Mathematics | Hilbert space | Engineering, general | Computer Science, general

34K50 | Approximate controllability | Fixed point theorem | Fractional stochastic differential systems | 93E03 | 93B05 | Poisson jumps | Mathematics, general | Mathematics | Hilbert space | Engineering, general | Computer Science, general

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2017, Volume 2017, Issue 1, pp. 1 - 15

A stochastic predator-prey system with time-dependent delays is considered. Firstly, we show the existence of a global positive solution and stochastically...

prey-predator system | Mathematics | Ordinary Differential Equations | extinction | Functional Analysis | 92B05 | 92D25 | 93E03 | Analysis | Difference and Functional Equations | Mathematics, general | stochastically ultimate bounded | persistence | time-dependent delays | Partial Differential Equations | MATHEMATICS, APPLIED | GLOBAL STABILITY | RANDOM PERTURBATION | MATHEMATICS | LOGISTIC EQUATION | SYSTEMS | DIFFUSION | COMPETITIVE MODEL | Functions of bounded variation | Theorems (Mathematics) | Usage | Computer simulation | Time dependence | Extinction

prey-predator system | Mathematics | Ordinary Differential Equations | extinction | Functional Analysis | 92B05 | 92D25 | 93E03 | Analysis | Difference and Functional Equations | Mathematics, general | stochastically ultimate bounded | persistence | time-dependent delays | Partial Differential Equations | MATHEMATICS, APPLIED | GLOBAL STABILITY | RANDOM PERTURBATION | MATHEMATICS | LOGISTIC EQUATION | SYSTEMS | DIFFUSION | COMPETITIVE MODEL | Functions of bounded variation | Theorems (Mathematics) | Usage | Computer simulation | Time dependence | Extinction

Journal Article

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