• Previous Article
    Explicit transport semigroup associated to abstract boundary conditions
  • PROC Home
  • This Issue
  • Next Article
    Characterisation of the asymptotic behaviour of scalar linear differential equations with respect to a fading stochastic perturbation
2011, 2011(Special): 91-101. doi: 10.3934/proc.2011.2011.91

Exponential growth in the solution of an affine stochastic differential equation with an average functional and financial market bubbles

1. 

Edgeworth Centre for Financial Mathematics, School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland, Ireland

Received  July 2010 Revised  June 2011 Published  October 2011

We consider an ane stochastic di erential equation with an av- erage functional. In our main results, we determine the asymptotic rate of growth of the mean of the solution of this functional di erential equation, and show that the solution of the equation has the same asymptotic rate of growth, almost surely.
Citation: John A. D. Appleby, John A. Daniels. Exponential growth in the solution of an affine stochastic differential equation with an average functional and financial market bubbles. Conference Publications, 2011, 2011 (Special) : 91-101. doi: 10.3934/proc.2011.2011.91
[1]

Reza Chaharpashlou, Abdon Atangana, Reza Saadati. On the fuzzy stability results for fractional stochastic Volterra integral equation. Discrete and Continuous Dynamical Systems - S, 2021, 14 (10) : 3529-3539. doi: 10.3934/dcdss.2020432

[2]

Hermann Brunner, Chunhua Ou. On the asymptotic stability of Volterra functional equations with vanishing delays. Communications on Pure and Applied Analysis, 2015, 14 (2) : 397-406. doi: 10.3934/cpaa.2015.14.397

[3]

Eleonora Messina. Numerical simulation of a SIS epidemic model based on a nonlinear Volterra integral equation. Conference Publications, 2015, 2015 (special) : 826-834. doi: 10.3934/proc.2015.0826

[4]

Pengyu Chen, Xuping Zhang, Yongxiang Li. A blowup alternative result for fractional nonautonomous evolution equation of Volterra type. Communications on Pure and Applied Analysis, 2018, 17 (5) : 1975-1992. doi: 10.3934/cpaa.2018094

[5]

T. Diogo, P. Lima, M. Rebelo. Numerical solution of a nonlinear Abel type Volterra integral equation. Communications on Pure and Applied Analysis, 2006, 5 (2) : 277-288. doi: 10.3934/cpaa.2006.5.277

[6]

Noui Djaidja, Mostefa Nadir. Comparison between Taylor and perturbed method for Volterra integral equation of the first kind. Numerical Algebra, Control and Optimization, 2021, 11 (4) : 487-493. doi: 10.3934/naco.2020039

[7]

Anna Karczewska, Carlos Lizama. On stochastic fractional Volterra equations in Hilbert space. Conference Publications, 2007, 2007 (Special) : 541-550. doi: 10.3934/proc.2007.2007.541

[8]

T. Diogo, N. B. Franco, P. Lima. High order product integration methods for a Volterra integral equation with logarithmic singular kernel. Communications on Pure and Applied Analysis, 2004, 3 (2) : 217-235. doi: 10.3934/cpaa.2004.3.217

[9]

Seiyed Hadi Abtahi, Hamidreza Rahimi, Maryam Mosleh. Solving fuzzy volterra-fredholm integral equation by fuzzy artificial neural network. Mathematical Foundations of Computing, 2021, 4 (3) : 209-219. doi: 10.3934/mfc.2021013

[10]

Miloud Moussai. Application of the bernstein polynomials for solving the nonlinear fractional type Volterra integro-differential equation with caputo fractional derivatives. Numerical Algebra, Control and Optimization, 2022, 12 (3) : 551-568. doi: 10.3934/naco.2021021

[11]

Michel Benaïm, Antoine Bourquin, Dang H. Nguyen. Stochastic persistence in degenerate stochastic Lotka-Volterra food chains. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022023

[12]

Chunhong Li, Jiaowan Luo. Stochastic invariance for neutral functional differential equation with non-lipschitz coefficients. Discrete and Continuous Dynamical Systems - B, 2019, 24 (7) : 3299-3318. doi: 10.3934/dcdsb.2018321

[13]

Defei Zhang, Ping He. Functional solution about stochastic differential equation driven by $G$-Brownian motion. Discrete and Continuous Dynamical Systems - B, 2015, 20 (1) : 281-293. doi: 10.3934/dcdsb.2015.20.281

[14]

Tomás Caraballo, María J. Garrido–Atienza, Björn Schmalfuss, José Valero. Asymptotic behaviour of a stochastic semilinear dissipative functional equation without uniqueness of solutions. Discrete and Continuous Dynamical Systems - B, 2010, 14 (2) : 439-455. doi: 10.3934/dcdsb.2010.14.439

[15]

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

[16]

Yufeng Shi, Tianxiao Wang, Jiongmin Yong. Mean-field backward stochastic Volterra integral equations. Discrete and Continuous Dynamical Systems - B, 2013, 18 (7) : 1929-1967. doi: 10.3934/dcdsb.2013.18.1929

[17]

Rui Wang, Xiaoyue Li, Denis S. Mukama. On stochastic multi-group Lotka-Volterra ecosystems with regime switching. Discrete and Continuous Dynamical Systems - B, 2017, 22 (9) : 3499-3528. doi: 10.3934/dcdsb.2017177

[18]

Fulvia Confortola, Elisa Mastrogiacomo. Feedback optimal control for stochastic Volterra equations with completely monotone kernels. Mathematical Control and Related Fields, 2015, 5 (2) : 191-235. doi: 10.3934/mcrf.2015.5.191

[19]

Tianxiao Wang, Yufeng Shi. Symmetrical solutions of backward stochastic Volterra integral equations and their applications. Discrete and Continuous Dynamical Systems - B, 2010, 14 (1) : 251-274. doi: 10.3934/dcdsb.2010.14.251

[20]

Yufeng Shi, Tianxiao Wang, Jiongmin Yong. Optimal control problems of forward-backward stochastic Volterra integral equations. Mathematical Control and Related Fields, 2015, 5 (3) : 613-649. doi: 10.3934/mcrf.2015.5.613

 Impact Factor: 

Metrics

  • PDF downloads (48)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]