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## HJB equations with gradient constraint associated with controlled jump-diffusion processes

SIAM Journal on Control and Optimization. 2019. Vol. 57. No. 3. P. 2185-2213.

In this paper, we guarantee the existence and uniqueness (in the almost everywhere

sense) of the solution to a Hamilton-Jacobi-Bellman (HJB) equation with gradient

constraint and a partial integro-di erential operator whose Levy measure has bounded

variation. This type of equation arises in a singular control problem, where the state

process is a multidimensional jump-di usion with jumps of finite variation and infinite

activity. We verify, by means of "-penalized controls, that the value function associated

with this problem satis es the aforementioned HJB equation.

Presnova A., Journal of Physics: Conference Series 2019 No. 1163 P. 1-6

The mathematical model describing the dynamics of HIV in the human body is a nonlinear system of differential equations. This model takes into account the effect of drugs on the body. Thus, it is possible to obtain ”optimal” treatment regimens for patients, which cause minimal harm to the body. In the work for constructing suboptimal ...

Added: March 28, 2019

Presnova A., Автоматизация. Современные технологии 2018 Т. 72 № 12 С. 563-569

The problem of searching for optimal control of nonlinear systems is indicated. Using the algorithmic method proposed in this paper, suboptimal control of a nonlinear object is constructed. The necessary assumptions are made for using the method of extended linearization. The example demonstrates the work of an algorithmic method for synthesizing suboptimal controls, and compares ...

Added: October 2, 2018

Kelbert M., Moreno-Franco H. A., Advances in Applied Probability 2022 Vol. 54 No. 3 P. 743-782

This paper studies a mixed singular/switching stochastic control problem for a
multidimensional diusion with multiple regimes on a bounded domain. Using
probabilistic, partial dierential equation (PDE) and penalization techniques,
we show that the value function associated with this problem agrees with the
solution to a Hamilton-Jacobi-Bellman (HJB) equation. In that way, we see
that the regularity of the value function ...

Added: September 26, 2021

Lubashevsky I., Friedrich R., Heuer A., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2009 Vol. 80 Article 031148

The paper presents a multidimensional model for nonlinear Markovian random walks that generalizes the one we developed previously [I. Lubashevsky, R. Friedrich, and A. Heuer, Phys. Rev. E 79, 011110 (2009)] in order to describe the Lévy-type stochastic processes in terms of continuous trajectories of walker motion. This approach may open a way to treat ...

Added: November 6, 2021

Kelbert M., Karpikov I., Science and Business: Ways of Development 2018 Vol. 79 No. 1 P. 56-68

This article gives a brief summary on the main theoretical and practical results for the Scale functions. The article is organized in the following way: the first part describes the main theoretical concepts of Lévy processes, gives the formal definition and analytical properties of the Scale function. The second part describes the most significant practical ...

Added: April 5, 2018

Belomestny D., Trabs M., Annales de l'institut Henri Poincare (B) Probability and Statistics 2018 Vol. 54 No. 3 P. 1583-1621

The estimation of the diffusion matrix Σ of a high-dimensional, possibly time-changed Levy process is studied, based on discrete observations of the process with a fixed distance. A low-rank condition is imposed on Σ. Applying a spectral approach, we construct a weighted least-squares estimator with nuclear-norm-penalisation. We prove oracle inequalities and derive convergence rates for ...

Added: May 5, 2018

Lubashevsky I., Heuer A., Friedrich R. et al., The European Physical Journal B 2010 Vol. 78 P. 207-216

We consider a previously devised model describing Lévy random walks [I. Lubashevsky, R. Friedrich, A. Heuer, Phys. Rev. E 79, 011110 (2009); I. Lubashevsky, R. Friedrich, A. Heuer, Phys. Rev. E 80, 031148 (2009)]. It is demonstrated numerically that the given model describes Lévy random walks with superdiffusive, ballistic, as well as superballistic dynamics. Previously ...

Added: November 6, 2021

Manita A., Journal of Physics: Conference Series 2016 Vol. 681 No. 1 P. 1-6

We consider N-component synchronization models defined in terms of stochastic particle systems with special interaction. For general (nonsymmetric) Markov models we discuss phenomenon of the long time stochastic synchronization. We study behavior of the system in different limit situations related to appropriate changes of variables and scalings. For N = 2 limit distributions are found ...

Added: March 29, 2016

Manita A., Intrinsic scales for high-dimensional Levy-driven models with non-Markovian synchronizing updates / Cornell University. Series "Working papers by Cornell University". 2014. No. arXiv:1409.2919.

http://xxx.tau.ac.il/abs/1409.2919 We propose stochastic N -component synchronization models, whose dynamics is described by Levy processes and synchronizing jumps. We prove that symmetric models reach synchronization in a stochastic sense: differences between components have limits in distribution as t→∞. We give conditions of existence of natural (intrinsic) space scales for large synchronized systemsю. It appears that ...

Added: March 18, 2015

Lubashevsky I., Friedrich R., Heuer A., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2009 Vol. 79 Article 011110

Based on multivariate Langevin processes we present a realization of Lévy flights as a continuous process. For the simple case of a particle moving under the influence of friction and a velocity-dependent stochastic force we explicitly derive the generalized Langevin equation and the corresponding generalized Fokker-Planck equation describing Lévy flights. Our procedure is similar to ...

Added: November 6, 2021

Moreno-Franco H. A., Applied Mathematics and Optimization 2018 Vol. 78 No. 1 P. 25-60

The main goal of this paper is to establish existence, regularity and uniqueness results for the solution of a Hamilton–Jacobi–Bellman (HJB) equation, whose operator is an elliptic integro-differential operator. The HJB equation studied in this work arises in singular stochastic control problems where the state process is a controlled d-dimensional Lévy process. ...

Added: October 12, 2016

Gromov D., Bondarev A., Gromova E., Optimization Letters 2021

In this contribution, we consider the optimal control problem for a switched dynamical system. While such systems can exhibit rather complex behavior in the case of only one switch, the most interesting problem corresponds to the case, when the system undergoes an infinite number of switches. We study the limiting behavior of optimal solutions under ...

Added: October 8, 2021

Junca M., Harold A. Moreno-Franco, Pérez J., Risks 2019 Vol. 7 No. 1 Article 13

We consider the optimal bail-out dividend problem with fixed transaction cost for a Lévy risk model with a constraint on the expected present value of injected capital. To solve this problem, we first consider the optimal bail-out dividend problem with transaction cost and capital injection and show the optimality of reflected (c_1,c_2) -policies. We then ...

Added: September 27, 2019

Max press, 2018

This collection of articles contain materials of the talks presented at the International Conference "Systems Analysis: Modeling and Control" in memory of Academician A.V. Kryazhimskiy, Moscow, May 31 - June 1, 2018 ...

Added: June 18, 2018

Lubashevsky I., The European Physical Journal B 2010 Vol. 82 P. 189-195

A continuous Markovian model for truncated Lévy flights is proposed. It generalizes the approach developed previously by Lubashevsky et al. [Phys. Rev. E 79, 011110 (2009); Phys. Rev. E 80, 031148 (2009), Eur. Phys. J. B 78, 207 (2010)] and allows for nonlinear friction in wandering particle motion as well as saturation of the noise intensity ...

Added: November 6, 2021

Junca M., Moreno-Franco H. A., Pérez J. et al., Advances in Applied Probability 2019 Vol. 51 No. 3 P. 633-666

We consider de Finetti’s problem for spectrally one-sided Lévy risk models with control strategies that are absolutely continuous with respect to the Lebesgue measure. Furthermore, we consider the version with a constraint on the time of ruin. To characterize the solution to the aforementioned models, we first solve the optimal dividend problem with a terminal ...

Added: March 25, 2018

M. : Steklov Mathematical Institute, 2022

This collection of articles contains materials of the talks presented at the International Conference dedicated to the centenary of the birth of Academician Evgenii Frolovich Mishchenko, Moscow, June 7–9, 2022 ...

Added: January 31, 2023

Lubashevsky I., Physica A: Statistical Mechanics and its Applications 2013 Vol. 392 No. 10 P. 2323-2346

The paper is devoted to the relationship between the continuous Markovian description of Lévy flights developed previously (see, e.g., I.A. Lubashevsky, Truncated Lévy flights and generalized Cauchy processes, Eur. Phys. J. B 82 (2011) 189–195 and references therein) and their equivalent representation in terms of discrete steps of a wandering particle, a certain generalization of ...

Added: November 6, 2021

Manita A., Journal of Physics: Conference Series 2019 Vol. 1163 No. 012060 P. 1-7

L´evy stochastic processes and related fine analytic properties of probability distributions such as infinite divisibility play an important role in construction of stochastic models of various distributed networks (e.g., local clock synchronization), of some physical systems (e.g., anomalous diffusions, quantum probability models), of finance etc. Nevertheless, little is known about limit probability laws resulted from ...

Added: June 21, 2019

Furmanov K. K., Nikol'skii I. M., Computational Mathematics and Modeling 2016 Vol. 27 No. 2 P. 247-253

Added: December 22, 2016

Sirotin V., Arkhipova M., Dubrova T. A. et al., Bielsko-Biala : University of Bielsko-Biala Press, 2016

The main attributes of modern enterprises should be the flexibility and the ability of forecasting the future. Constant adaptation to the changing environment and the rapidity of undertaking certain actions which are conditioned by specific situations determine the rules for the future position of market competition. Effective and efficient adjustment of the company in line ...

Added: November 2, 2016

Litvin Y. V., Абрамов И. В., Технологии техносферной безопасности 2016 № 66

Advanced approach to the assessment of a random time of arrival fire fighting calculation on the object of protection, the time of their employment and the free combustion. There is some quantitative assessments with the review of analytical methods and simulation ...

Added: August 27, 2016

Maslov V., Теоретическая и математическая физика 2019 Т. 201 № 1 С. 65-83

We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
using experimental values of the binding energy for the nucleus of the given substance. A nucleon becomes
a boson at the instant of separating from a fermionic nucleus. We study the further transformations of
boson and fermion states of separation in a ...

Added: November 1, 2019

Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18

Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...

Added: November 16, 2020