American Institute of Mathematical Sciences

Advanced
September  2007, 8(2): 511-527. doi: 10.3934/dcdsb.2007.8.511

Generators of Feller semigroups with coefficients depending on parameters and optimal estimators

Jerome A. Goldstein 1, , Rosa Maria Mininni 2, and  Silvia Romanelli 2,

1. 

Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, United States
2. 

Dipartimento di Matematica, Università degli Studi di Bari, Via Orabona, 4, 70125 Bari, Italy, Italy

Received  September 2006 Revised  February 2007 Published  June 2007

We consider the realization of the operator $L_{\theta, a}u(x) $:$= x^{2 a}u''(x) \ + \ (a x^{2 a - 1} + \theta x^a)u'(x)$, acting on $C[0,+\infty]$, for $\theta\in\R$, $a\in\R$. We show that $L_{\theta, a}$, with the so called Wentzell boundary conditions, generates a Feller semigroup for any $\theta\in\R$, $a\in\R$. The problem of finding optimal estimators for the corresponding diffusion processes is also discussed, in connection with some models in financial mathematics. Here $C[0,+\infty]$ is the space of all real valued continuous functions on $[0,+\infty)$ which admit finite limit at $+\infty$.
Keywords: stochastic differential equations, optimal estimators., diffusion processes, Feller semigroups, operator semigroups.
Mathematics Subject Classification: Primary: 47D07, 60J60, 62M05; Secondary: 60H10, 91B7.
Citation: Jerome A. Goldstein, Rosa Maria Mininni, Silvia Romanelli. Generators of Feller semigroups with coefficients depending on parameters and optimal estimators. Discrete & Continuous Dynamical Systems - B, 2007, 8 (2) : 511-527. doi: 10.3934/dcdsb.2007.8.511
[1]

Lavinia Roncoroni. Exact lumping of feller semigroups: A $C^{\star}$-algebras approach. Conference Publications, 2015, 2015 (special) : 965-973. doi: 10.3934/proc.2015.0965
[2]

András Bátkai, Istvan Z. Kiss, Eszter Sikolya, Péter L. Simon. Differential equation approximations of stochastic network processes: An operator semigroup approach. Networks & Heterogeneous Media, 2012, 7 (1) : 43-58. doi: 10.3934/nhm.2012.7.43
[3]

Katarzyna Pichór, Ryszard Rudnicki. Applications of stochastic semigroups to cell cycle models. Discrete & Continuous Dynamical Systems - B, 2019, 24 (5) : 2365-2381. doi: 10.3934/dcdsb.2019099
[4]

Katarzyna PichÓr, Ryszard Rudnicki. Stability of stochastic semigroups and applications to Stein's neuronal model. Discrete & Continuous Dynamical Systems - B, 2018, 23 (1) : 377-385. doi: 10.3934/dcdsb.2018026
[5]

Francesco Altomare, Mirella Cappelletti Montano, Vita Leonessa. On the positive semigroups generated by Fleming-Viot type differential operators. Communications on Pure & Applied Analysis, 2019, 18 (1) : 323-340. doi: 10.3934/cpaa.2019017
[6]

Zdzisław Brzeźniak, Paul André Razafimandimby. Irreducibility and strong Feller property for stochastic evolution equations in Banach spaces. Discrete & Continuous Dynamical Systems - B, 2016, 21 (4) : 1051-1077. doi: 10.3934/dcdsb.2016.21.1051
[7]

Jacek Banasiak, Mustapha Mokhtar-Kharroubi. Universality of dishonesty of substochastic semigroups: Shattering fragmentation and explosive birth-and-death processes. Discrete & Continuous Dynamical Systems - B, 2005, 5 (3) : 529-542. doi: 10.3934/dcdsb.2005.5.529
[8]

Angela A. Albanese, Elisabetta M. Mangino. Analytic semigroups and some degenerate evolution equations defined on domains with corners. Discrete & Continuous Dynamical Systems - A, 2015, 35 (2) : 595-615. doi: 10.3934/dcds.2015.35.595
[9]

Horst R. Thieme. Positive perturbation of operator semigroups: growth bounds, essential compactness and asynchronous exponential growth. Discrete & Continuous Dynamical Systems - A, 1998, 4 (4) : 735-764. doi: 10.3934/dcds.1998.4.735
[10]

Fritz Colonius, Marco Spadini. Fundamental semigroups for dynamical systems. Discrete & Continuous Dynamical Systems - A, 2006, 14 (3) : 447-463. doi: 10.3934/dcds.2006.14.447
[11]

José A. Conejero, Alfredo Peris. Chaotic translation semigroups. Conference Publications, 2007, 2007 (Special) : 269-276. doi: 10.3934/proc.2007.2007.269
[12]

Min He. On continuity in parameters of integrated semigroups. Conference Publications, 2003, 2003 (Special) : 403-412. doi: 10.3934/proc.2003.2003.403
[13]

Alastair Fletcher. Quasiregular semigroups with examples. Discrete & Continuous Dynamical Systems - A, 2019, 39 (4) : 2157-2172. doi: 10.3934/dcds.2019090
[14]

Vladimir Kazakov. Sampling - reconstruction procedure with jitter of markov continuous processes formed by stochastic differential equations of the first order. Conference Publications, 2009, 2009 (Special) : 433-441. doi: 10.3934/proc.2009.2009.433
[15]

Agnieszka Bartłomiejczyk, Henryk Leszczyński. Structured populations with diffusion and Feller conditions. Mathematical Biosciences & Engineering, 2016, 13 (2) : 261-279. doi: 10.3934/mbe.2015002
[16]

Yuri Latushkin, Valerian Yurov. Stability estimates for semigroups on Banach spaces. Discrete & Continuous Dynamical Systems - A, 2013, 33 (11&12) : 5203-5216. doi: 10.3934/dcds.2013.33.5203
[17]

Jeremy LeCrone, Gieri Simonett. Continuous maximal regularity and analytic semigroups. Conference Publications, 2011, 2011 (Special) : 963-970. doi: 10.3934/proc.2011.2011.963
[18]

Sebastián Donoso. Enveloping semigroups of systems of order d. Discrete & Continuous Dynamical Systems - A, 2014, 34 (7) : 2729-2740. doi: 10.3934/dcds.2014.34.2729
[19]

Samir EL Mourchid. On a hypercylicity criterion for strongly continuous semigroups. Discrete & Continuous Dynamical Systems - A, 2005, 13 (2) : 271-275. doi: 10.3934/dcds.2005.13.271
[20]

Edmond W. H. Lee. Equational theories of unstable involution semigroups. Electronic Research Announcements, 2017, 24: 10-20. doi: 10.3934/era.2017.24.002

2018 Impact Factor: 1.008

Tools

Metrics

  • PDF downloads (10)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences