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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
Journal Article
The Annals of Probability, ISSN 0091-1798, 5/2009, Volume 37, Issue 3, pp. 877 - 902
Journal Article
Journal of Applied Probability, ISSN 0021-9002, 06/2015, Volume 52, Issue 2, pp. 508 - 518
We show how to determine if a given vector can be the signature of a system on a finite number of components and, if so, exhibit such a system in terms of its... 
60C05 | 93E03 | simplicial complexes | Signature | reliability
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
Journal Article
Stochastic Analysis and Applications, ISSN 0736-2994, 01/2013, Volume 31, Issue 1, pp. 142 - 166
In this article, a class of linear backward stochastic differential equations of descriptor type with time-invariant coefficients are introduced. Necessary and... 
BSDEs | Exact controllability | Descriptor systems | Solvability | 93E03, 34K50, 15A22 | MATHEMATICS, APPLIED | 34K50 | 93E03 | 15A22 | COEFFICIENTS | STATISTICS & PROBABILITY | CONTROLLABILITY | Control systems | Controllability | Stochasticity | Terminals | Mathematical analysis | Differential equations
Journal Article
International Journal of Control, ISSN 0020-7179, 08/2017, Volume 90, Issue 8, pp. 1597 - 1603
Journal Article
Applicable Analysis, ISSN 0003-6811, 11/2016, Volume 95, Issue 11, pp. 2361 - 2382
Journal Article
Journal of Applied Probability, ISSN 0021-9002, 09/2015, Volume 52, Issue 3, pp. 718 - 735
In a defaultable market, an investor trades having only partial information about the behavior of the market. Taking into account the intraday stock movements,... 
93E11 | Optimal investment | 49L20 | 93E03 | dynamic programming | default time | exponential utility | filtering | backward stochastic differential equation
Journal Article
Fractional Calculus and Applied Analysis, ISSN 1311-0454, 10/2016, Volume 19, Issue 5, pp. 1282 - 1291
The only purpose of this paper is to show how fractional calculus can contribute to the development of the very interesting and promising field of micro and... 
fractional calculus | medical application | microrobot | Primary 26A33 | Secondary 60G22, 93E03, 35Q30, 34M03 | Brownian motor
Journal Article
Statistics and Probability Letters, ISSN 0167-7152, 06/2017, Volume 125, pp. 1 - 8
General stochastic Euler schemes for ordinary differential equations are studied. We give proofs on the consistency, the rate of convergence and the asymptotic... 
Ordinary differential equations | Rate of convergence | Asymptotic normality | Consistency | Stochastic Euler schemes | STATISTICS & PROBABILITY
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
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
Journal Article
Electronic Communications in Probability, ISSN 1083-589X, 2017, Volume 22
We provide necessary and sufficient first order geometric conditions for the stochastic invariance of a closed subset of R-d with respect to a jump-diffusion... 
Jumps | Stochastic invariance | Semimartingale | Stochastic differential equation | MARTINGALES | stochastic differential equation | semimartingale | jumps | SYSTEMS | STATISTICS & PROBABILITY | stochastic invariance | Probability | Mathematics
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
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
Journal Article
数学物理学报:B辑英文版, ISSN 0252-9602, 2016, Volume 36, Issue 5, pp. 1509 - 1523
This paper has two sections which deals with a second order stochastic neutral partial differential equation with state dependent delay. In the first section... 
approximate controllability | 35R60 | measure of noncompactness | 93E03 | 93B05 | cosine family | state dependent delay | neutral stochastic differential equation | 35R15 | UNBOUNDED DELAY | MATHEMATICS | SPACES | SYSTEMS
Journal Article
International Journal of Control, ISSN 0020-7179, 05/2009, Volume 82, Issue 5, pp. 801 - 807
In this article, we consider the finite-dimensional dynamical control systems described by non-linear impulsive stochastic differential equations. Sufficient... 
Brownian motion | 93E20 | complete and approximate controllability | 93E03 | 93B05 | resolvent operators | impulsive stochastic systems | Impulsive stochastic systems | Complete and approximate controllability | Resolvent operators | EXISTENCE | SPACES | STABILITY | CALCULUS | AUTOMATION & CONTROL SYSTEMS | UNIQUENESS
Journal Article
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