Asymptotics for time-changed diffusions
Authors:
Raffaela Capitanelli and Mirko D’Ovidio
Journal:
Theor. Probability and Math. Statist. 95 (2017), 41-58
MSC (2010):
Primary 60J65, 60J50, 35J25
DOI:
https://doi.org/10.1090/tpms/1021
Published electronically:
February 28, 2018
MathSciNet review:
3631643
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References |
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Additional Information
Abstract: We consider time-changed diffusions driven by generators with discontinuous coefficients. The PDE’s connections are investigated, and in particular some results on the asymptotic analysis according to the behaviour of the coefficients are presented.
References
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References
- T. Appuhamillage, V. Bokil, E. Thomann, E. Waymire, and B. Wood, Occupation and local times for skew Brownian motion with applications to dispersion across an interface, Ann. Appl. Probab. 21 (2011), no. 1, 183–214. MR 2759199
- E. Acerbi and G. Buttazzo, Reinforcement problems in the calculus of variations, Ann. Inst. H. Poincaré Anal. Non Lin. 3 (1986), no. 4, 273–284. MR 853383
- H. Brezis, L. A. Caffarelli, and A. Friedman, Reinforcement problems for elliptic equations and variational inequalities, Ann. Mat. Pura Appl. 123 (1980), no. 4, 219–246. MR 581931
- S. Blei, On symmetric and skew Bessel processes, Stochastic Processes and their Applications 122 (2012), 3262–3287. MR 2946442
- R. M. Blumenthal and R. K. Getoor, Markov Processes and Potential Theory, Academic Press, New York, 1968. MR 0264757
- R. Capitanelli and M. D’Ovidio, Skew Brownian diffusions across Koch interfaces, Potential Anal. (2016), doi: 10.1007/s11118-016-9588-4. MR 3630403
- R. Capitanelli and M. A. Vivaldi, On the Laplacean transfer across fractal mixtures, Asymptot. Anal. 83 (2013), no. 1–2, 1–33. MR 3100114
- M. Decamps, M. Goovaerts, and W. Schoutens, Asymmetric skew Bessel processes and their applications to finance, Journal of Computational and Applied Mathematics 186 (2006), 130–147. MR 2190302
- M. D’Ovidio, From Sturm–Liouville problems to fractional and anomalous diffusions, Stochastic Process. Appl. 122 (2012), no. 10, 3513–3544. MR 2956115
- J. M. Harrison and L. A. Shepp, On skew Brownian motion, Ann. Probab. 9 (1981), 309–313. MR 606993
- S. Karlin and H. M. Taylor, A Second Course in Stochastic Processes, Academic Press, New York, 1981. MR 611513
- K. Itô and H. P. McKean, Jr., Diffusion Processes and Their Sample Paths, Springer-Verlag, Heidelberg–New York, 1974. MR 0345224
- A. Lejay, On the constructions of the skew Brownian motion, Probab. Surveys 3 (2006), 413–466. MR 2280299
- N. N. Leonenko, M. M. Meerschaert, and A. Sikorskii, Fractional Pearson diffusions, J. Math. Anal. Appl. 403 (2013), no. 2, 532–546. MR 3037487
- N. N. Leonenko and N. Šuvak, Statistical inference for reciprocal gamma diffusion process, J. Statist. Plann. Inference 140 (2010), no. 1, 30–51. MR 2568120
- U. Mosco, Convergence of convex sets and of solutions of variational inequalities, Adv. in Math. 3 (1969), 510–585. MR 0298508
- U. Mosco, Composite media and asymptotic Dirichlet forms, J. Funct. Anal. 123 (1994), no. 2, 368–421. MR 1283033
- Y. Ouknine, F. Russo, and G. Trutnau, On countably skewed Brownian motion with accumulation point, Electron. J. Probab. 20 (2015), no. 82, 1–27. MR 3383566
- J. M. Ramirez, Multi-skewed Brownian motion and diffusion in layered media, Proceedings of the American Mathematical Society 139 (2011), 3739–3752. MR 2813404
- D. Revuz and M. Yor, Continuous martingales and Brownian motion, 3rd ed., Springer-Verlag, Berlin, 1999. MR 1725357
- J. B. Walsh, A diffusion with a discontinuous local time, Asterisque 52–53 (1978), 37–45.
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Additional Information
Raffaela Capitanelli
Affiliation:
Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sapienza" Università di Roma, Via A. Scarpa 16, 00161 Roma, Italy
Email:
raffaela.capitanelli@uniroma1.it
Mirko D’Ovidio
Affiliation:
Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sapienza" Università di Roma, Via A. Scarpa 16, 00161 Roma, Italy
Email:
mirko.dovidio@uniroma1.it
Keywords:
Skew Brownian motion,
scale function,
boundary value problems
Received by editor(s):
September 30, 2016
Published electronically:
February 28, 2018
Additional Notes:
The authors are members of GNAMPA (INdAM). The authors are partially supported by Grants Ateneo \lq\lq Sapienza” 2015.
Article copyright:
© Copyright 2018
American Mathematical Society