On nonautonomous Markov evolutions in continuum

M. Friesen, O. Kutoviy

Анотація


The nonautonomous Cauchy problem in a scale of Banach spaces is investigated. The existence and uniqueness of solutions to this problem is proven. The obtained results are applied to several dynamics of Markov evolutions in continuum (e.g.  spatial logistic model, Glauber dynamics, etc.).

Повний текст:

PDF (English)

Посилання


S. Albeverio, Y. G. Kondratiev, M. R¨ockner. Analysis and geometry on configuration spaces, J. Funct. Anal. (1998), 154(2): 444–500

O. Caps. Evolution Equations in Scales of Banach Spaces, Teubner, Stuttgart/Leipzig/Wiesbaden (2002)

D. Finkelshtein. Functional evolutions for homogeneous stationary death- immigration spatial dynamics, Methods Funct. Anal. Topology 17 (2011), no. 4: 300–318

D. Finkelshtein, Y. Kondratiev, Y. Kozitsky. Glauber Dynamics in Continuum: A Constructive Approach to Evolution of States, Discrete and Cont. Dynam. Syst. - Ser. A 33 (2013), no. 4: 1431–1450.

D. Finkelshtein, Y. Kondratiev, Y. Kozitsky, O. Kutoviy. Markov Evolution of Continuous Particle Systems with Dispersion and Competition, arXiv:1112.0895v2 [math-ph]

D. Finkelshtein, Y. Kondratiev, O. Kutoviy. Correlation functions evolution for the Glauber dynamics in continuum, Semigroup Forum 85 (2012), no. 2: 289–306

D. Finkelshtein, Y. Kondratiev, O. Kutoviy. Individual based model with competition in spatial ecology, J. MATH. ANAL. Vol. 41, No. 1, pp. 297– 317

D. Finkelshtein, Y. Kondratiev, O. Kutoviy. Semigroup approach to birth- and-death stochastic dynamics in continuum, J. Funct. Anal. 262 (2012), no. 3: 1274–1308

D. Finkelshtein, Y. Kondratiev, O. Kutoviy. Vlasov scaling for the Glauber dynamics in continuum, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 14 (2011), no. 4: 537–569

D. Finkelshtein, Y. Kondratiev, M. Oliveira. Markov evolutions and hierarchical equations in the continuum I. One-component systems, J. Evol. Equ. 9 (2009), no. 2: 197–233

D. Finkelshtein, Y. Kondratiev, M. Oliveira. Glauber dynamics in the continuum via generating functional evolution, Complex Anal. Oper. Theory 6 (2012), no. 4: 923–945

D. Finkelshtein, Y. Kondratiev, O. Kutoviy, E. Zhizhina An approximative approach for construction of the Glauber dynamics in continuum, Mathematische Nachrichten vol. 285 (2012), no. 2: 223–225

T. Kato. Linear evolution equations of hyperbolic type, II, J. Math. Soc.Japan Vol 25, No. 4 (1973)

Y. Kondratiev, T. Kuna. Harmonic Analysis on Configuration space I.General Theory, Infinite Dim. Analysis, Quantum Prob. and Related Topics (2002), Vol. 5, No. 2, 201–232

Y. Kondratiev, T. Kuna, M. Oliveira Holomorphic Bogoliubov functionals for interacting particle systems in continuum, Journal of Functional Analysis, 238 (2006): 375–404

Y. Kondratiev, O. Kutoviy, R. Minlos. On non-equilibrium stochastic dynamics for interacting particle systems in continuum, J. Funct. Anal. 255 (2008): 200–227

Y. Kondratiev, O. Kutoviy, E. Zhizhina. Nonequilibrium Glauber-type dynamics in continuum, J. Math. Phys. 47 (2006), 113501, 17

Y. Kondratiev, O. Kutoviy, S. Pirogov. Correlation functions and invariant measures in Continuous Contact Model, Inf. Dim. Analysis, Quantum Prob. and Related Topics (2008), Vol. 11, No. 2: 231–258

Y. Kondratiev, E. Lytvynov. Glauber dynamics of continuous particle systems, Ann. Inst. H: Poincare Probab. Statist. 41, no.4 (2005): 685–702

Y. Kondratiev, A. Skorohod. On Contact Processes in continuum, Inf. Dim. Analysis, Quantum Prob. and Related Topics (2006), Vol. 9, No. 2: 187–198

J. Neerven. The Adjoint of a Semigroup of Linear Operators, Springer-Verlag, Berlin-Heidelberg (1992), Lecture Notes in Mathematics 1529

G. Nickel. Evolutions Semigroups for Nonautonomous Cauchy Problems, Mancorp Publishing, Inc. (1996), 73–95

G. Nickel, R. Schnaubelt. An extension of Kato’s stability condition for nonatuonomous Cauchy Problems, Taiwanese Journal of Mathematics, Vol. 2, No. 4 (1998): 483–496

A. Pazy. Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer Verlag, New York (1983)

O. Pugachev. The Space of Simple Configurations is Polish, Mathematical Notes, Vol. 71 no. 4 (2002): 530–537

M. Safonov. The Abstract Cauchy-Kovalevskaya Theorem in a Weighted Banach Space, Communications on Pure and Applied Mathematics, Vol. XLVII (1995): 629–637

D. Surgailis. On Poisson multiple stochastic integrals and associated equilibrium Markov processes, in Theory and application of random fields (Bangalore 1982), vol. 49 of Lecture Notes in Control and Inform. Sci., Springer, Berlin, 1983: 233–248

D. Surgailis. On multiple Poisson stochastic integrals and associated Markov semigroups, Probab. Math. Statist., 4 (1984): 217–239


Пристатейна бібліографія ГОСТ




Посилання

  • Поки немає зовнішніх посилань.