The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off


  • Attanasio, Stefano; Flandoli, Franco. Zero-noise solutions of linear transport equations without uniqueness: an example. C. R. Math. Acad. Sci. Paris 347 (2009), no. 13-14, 753--756. MR2543977
  • Bafico, R.; Baldi, P. Small random perturbations of Peano phenomena. Stochastics 6 (1981/82), no. 3-4, 279--292. MR0665404
  • Banner, Adrian D.; Fernholz, Robert; Karatzas, Ioannis. Atlas models of equity markets. Ann. Appl. Probab. 15 (2005), no. 4, 2296--2330. MR2187296
  • Billingsley, Patrick. Convergence of probability measures. Second edition. Wiley Series in Probability and Statistics: Probability and Statistics. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1999. x+277 pp. ISBN: 0-471-19745-9 MR1700749
  • Bossy, Mireille; Talay, Denis. Convergence rate for the approximation of the limit law of weakly interacting particles: application to the Burgers equation. Ann. Appl. Probab. 6 (1996), no. 3, 818--861. MR1410117
  • Brenier, Yann; Grenier, Emmanuel. Sticky particles and scalar conservation laws. SIAM J. Numer. Anal. 35 (1998), no. 6, 2317--2328 (electronic). MR1655848
  • Buckdahn, R.; Ouknine, Y.; Quincampoix, M. On limiting values of stochastic differential equations with small noise intensity tending to zero. Bull. Sci. Math. 133 (2009), no. 3, 229--237. MR2512827
  • F. Delarue, F. Flandoli, and D. Vincenzi, Noise prevents collapse of Vlasov-Poisson point charges, Communications on Pure and Applied Mathematics (2013).
  • A. Dembo, M. Shkolnikov, S.R.S. Varadhan, and O. Zeitouni, Large deviations for diffusions interacting through their ranks, Preprint available at arXiv:1211.5223, 2012.
  • E, Weinan; Vanden-Eijnden, Eric. A note on generalized flows. Phys. D 183 (2003), no. 3-4, 159--174. MR2006631
  • Ethier, Stewart N.; Kurtz, Thomas G. Markov processes. Characterization and convergence. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. John Wiley & Sons, Inc., New York, 1986. x+534 pp. ISBN: 0-471-08186-8 MR0838085
  • Fernholz, E. Robert. Stochastic portfolio theory. Applications of Mathematics (New York), 48. Stochastic Modelling and Applied Probability. Springer-Verlag, New York, 2002. xiv+177 pp. ISBN: 0-387-95405-8 MR1894767
  • Fernholz, E. Robert; Ichiba, Tomoyuki; Karatzas, Ioannis; Prokaj, Vilmos. Planar diffusions with rank-based characteristics and perturbed Tanaka equations. Probab. Theory Related Fields 156 (2013), no. 1-2, 343--374. MR3055262
  • E. R. Fernholz and I. Karatzas, Stochastic portfolio theory: A survey, In Handbook of Numerical Analysis. Mathematical Modeling and Numerical Methods in Finance, 2009.
  • Fernholz, Robert; Ichiba, Tomoyuki; Karatzas, Ioannis. A second-order stock market model. Ann. Finance 9 (2013), no. 3, 439--454. MR3082660
  • Fleming, Wendell H.; Soner, H. Mete. Controlled Markov processes and viscosity solutions. Second edition. Stochastic Modelling and Applied Probability, 25. Springer, New York, 2006. xviii+429 pp. ISBN: 978-0387-260457; 0-387-26045-5 MR2179357
  • Freidlin, M. I.; Wentzell, A. D. Random perturbations of dynamical systems. Translated from the 1979 Russian original by Joseph Szücs. Second edition. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 260. Springer-Verlag, New York, 1998. xii+430 pp. ISBN: 0-387-98362-7 MR1652127
  • Gradinaru, Mihai; Herrmann, Samuel; Roynette, Bernard. A singular large deviations phenomenon. Ann. Inst. H. Poincaré Probab. Statist. 37 (2001), no. 5, 555--580. MR1851715
  • Herrmann, Samuel. Phénomène de Peano et grandes déviations. (French) [Large deviations for the Peano phenomenon] C. R. Acad. Sci. Paris Sér. I Math. 332 (2001), no. 11, 1019--1024. MR1838131
  • Ichiba, Tomoyuki; Karatzas, Ioannis. On collisions of Brownian particles. Ann. Appl. Probab. 20 (2010), no. 3, 951--977. MR2680554
  • Ichiba, Tomoyuki; Karatzas, Ioannis; Shkolnikov, Mykhaylo. Strong solutions of stochastic equations with rank-based coefficients. Probab. Theory Related Fields 156 (2013), no. 1-2, 229--248. MR3055258
  • Ichiba, Tomoyuki; Pal, Soumik; Shkolnikov, Mykhaylo. Convergence rates for rank-based models with applications to portfolio theory. Probab. Theory Related Fields 156 (2013), no. 1-2, 415--448. MR3055264
  • Ichiba, Tomoyuki; Papathanakos, Vassilios; Banner, Adrian; Karatzas, Ioannis; Fernholz, Robert. Hybrid atlas models. Ann. Appl. Probab. 21 (2011), no. 2, 609--644. MR2807968
  • Jourdain, B. Probabilistic approximation for a porous medium equation. Stochastic Process. Appl. 89 (2000), no. 1, 81--99. MR1775228
  • Jourdain, Benjamin. Particules collantes signées et lois de conservation scalaires 1D. (French) [Signed sticky particles and 1D scalar conservation laws] C. R. Math. Acad. Sci. Paris 334 (2002), no. 3, 233--238. MR1891065
  • Jourdain, Benjamin; Malrieu, Florent. Propagation of chaos and Poincaré inequalities for a system of particles interacting through their CDF. Ann. Appl. Probab. 18 (2008), no. 5, 1706--1736. MR2462546
  • B. Jourdain and J. Reygner, Propagation of chaos for rank-based interacting diffusions and long time behaviour of a scalar quasilinear parabolic equation, Stochastic Partial Differential Equations: Analysis and Computations 1 (2013), no. 3, 455--506 (English).
  • Karatzas, Ioannis; Shreve, Steven E. Trivariate density of Brownian motion, its local and occupation times, with application to stochastic control. Ann. Probab. 12 (1984), no. 3, 819--828. MR0744236
  • Karatzas, Ioannis; Shreve, Steven E. Brownian motion and stochastic calculus. Second edition. Graduate Texts in Mathematics, 113. Springer-Verlag, New York, 1991. xxiv+470 pp. ISBN: 0-387-97655-8 MR1121940
  • Pagès, Gilles. Sur quelques algorithmes récursifs pour les probabilités numériques. (French) [On some recursive algorithms for numerical probabilities] ESAIM Probab. Statist. 5 (2001), 141--170 (electronic). MR1875668
  • Pal, Soumik; Pitman, Jim. One-dimensional Brownian particle systems with rank-dependent drifts. Ann. Appl. Probab. 18 (2008), no. 6, 2179--2207. MR2473654
  • Revuz, Daniel; Yor, Marc. Continuous martingales and Brownian motion. Third edition. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 293. Springer-Verlag, Berlin, 1999. xiv+602 pp. ISBN: 3-540-64325-7 MR1725357
  • Rey-Bellet, Luc. Ergodic properties of Markov processes. Open quantum systems. II, 1--39, Lecture Notes in Math., 1881, Springer, Berlin, 2006. MR2248986
  • Stroock, Daniel W.; Varadhan, S. R. Srinivasa. Multidimensional diffusion processes. Reprint of the 1997 edition. Classics in Mathematics. Springer-Verlag, Berlin, 2006. xii+338 pp. ISBN: 978-3-540-28998-2; 3-540-28998-4 MR2190038
  • Tanaka, Hiroshi. Stochastic differential equations with reflecting boundary condition in convex regions. Hiroshima Math. J. 9 (1979), no. 1, 163--177. MR0529332
  • Veretennikov, A. Ju. Strong solutions and explicit formulas for solutions of stochastic integral equations. (Russian) Mat. Sb. (N.S.) 111(153) (1980), no. 3, 434--452, 480. MR0568986
  • Veretennikov, A. Yu. Approximation of ordinary differential equations by stochastic ones. (Russian) Mat. Zametki 33 (1983), no. 6, 929--932. MR0709231

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.