D Khoshnevisan's Publications (by year)
Last update: January 18, 2013

Books:

  1. A Minicourse on Stochastic Partial Differential Equations
    Springer-Verlag, Berlin (2008); (editor and chapter author; coeditor: Firas Rassoul-Agha; coauthors: Robert Dalang; Carl Mueller; David Nualart; and Yimin Xiao).
  2. Probability
    American Mathematical Society, Providence, Rhode Island (2007).
  3. Multiparameter Processes: An Introduction to Random Fields
    Springer, New York (2002).

To Appear/In Press:

  1. Hitting probabilities for systems of non-linear stochastic heat equations in spatial dimention \(k\ge1\)
    (49 pages; to appear in Stochastic Partial Differential Equations: Analysis and Computations; with Robert C. Dalang and Eulalia Nualart).
  2. On the chaotic character of the stochastic heat equation, II
    (46 pages; to appear in Probability Th. Rel. Fields; with Daniel Conus, Mathew Joseph, and Shang-Yuan Shiu).
  3. On the chaotic character of the stochastic heat equation, before the onset of intermittency
    (37 pages; to appear in "Ann. Probab."; with D. Conus and M. Joseph)
  4. Initial measures for the stochastic heat equation
    (23 pages; to appear in Annales Instit. Henri Poincaré; with Daniel Conus, Mathew Joseph, and Shang-Yuan Shiu).
  5. Weak nonmild solutions to some SPDEs
    (to appear in "Illinois J. of Math."; with Daniel Conus)

Journal Publications Starting From
2013

  1. On the stochastic heat equation with spatially-colored random forcing
    (with M. Foondun) Trans. Amer. Math. Soc. 365(1) 409-458.

2012

  1. Correlation-length bounds, and estimates for intermittent islands in parabolic SPDEs
    (with Daniel Conus and Mathew Joseph) Electronic Journal of Probability Vol. 17, Paper 102 (15 pp).
  2. Packing dimension profiles and Lévy processes
    (with René Schilling and Yimin Xiao) Bull. London Math. Soc. 44 931-943.
  3. An asymptotic theory for randomly-forced discrete nonlinear heat equations
    (with Mohammud Foondun) Bernoulli 18(3) 1042-1060.
  4. On the existence and position of the farthest peaks of a family of stochastic heat and wave equations
    (with Daniel Conus) Probab. Theory Rel. Fields 152(3-4) 681-701
  5. Critical Brownian sheet does not have double points
    (with R.C. Dalang, E. Nualart, D. Wu, and Y. Xiao) Ann. Probab. 40 (4) 1829-1859.

2011

  1. Charged polymers in the attractive regime: a first order transition from Brownian scaling to four-point localization
    (with Y. Hu and M. Wouts) J. Statist. Physics, 144(5) (2011), pp. 948--977.
  2. Dynkin's isomorphism theorem and the stochastic heat equation
    (with N. Eisenbaum and M. Foondun) Potential Analysis, 34 (2011), no. 3, pp. 243-260.
  3. A local-time correspondence for stochastic partial differential equations
    (with Mohammud Foondun and Eulalia Nualart) The Transactions of the AMS, Vol. 363 (5) 2481-2515.

2010

  1. On the global maximum of the solution to the stochastic heat equation with compact-support initial data
    (with Mohammud Foondun) Ann. Inst. Henri Poincaré Probab. Stat. 46(4) 895-907.
  2. Strong approximations in a charged-polymer model
    (with Yueyun Hu) Periodica Mathematica Hungarica, Vol. 61(1-2) 213-224.
  3. Zeros of a two-parameter random walk
    (with P. Révész) In "Dependence in Probability, Analysis, and Number Theory," 265-278 (I. Berkes, R. C. Bradley, H. Dehling, M. Peligrad, and R. Tichy, editors) Kendrick Press, Heber City.

2009

  1. Charged polymers and random walk in random scenery
    (with Xia Chen) In: Optimality: The Third Erich L. Lehmann Symposium, IMS Lecture Notes-Monograph Series, Vol. 57 (Javier Rojo, Editor), 237-251, IMS, Hayward, California.
  2. Harmonic analysis of additive Lévy processes
    (with Yimin Xiao) Probability Theory and Related Fields 145, 459-515.
  3. From fractals and probability to Lévy processes and stochastic PDEs
    Progress in Probability, Vol. 61, 111-141 (mostly a Survey).
  4. Hitting probabilities for systems of nonlinear stochastic heat equations with multiplicative noise
    (with Robert C. Dalang and Eulalia Nualart) Probability Theory and Related Fields 177, 371-427.
  5. Intermittence and nonlinear stochastic partial differential equations
    (with Mohammud Foondun) Electronic J. Probab. Vol. 14, Paper no. 21, 548-568.

2008

  1. Capacities in Wiener space, quasi-sure lower functions, and Kolmogorov's ε-entropy
    (with David A. Levin and Pedro J. Méndez-Hernández) Stochastic Proc. Appl.
    2. 118 no. 10, 1723-1737.
  2. Level sets of the stochastic wave equation driven by a symmetric Lévy noise.
    (with Eulalia Nualart) Bernoulli 14, 899-925.
  3. Packing-dimension profiles and fractional Brownian motion. (with Yimin Xiao)
    The Math. Proc. Cambridge Phil. Soc. 145, no. 1, 205-213.
  4. Packing dimension of the range of a Lévy process. (with Yimin Xiao)
    The Proceedings of the AMS, Vol. 136, No. 7, 2597-2607.
  5. Slices of the Brownian sheet: New results and open problems.
    Stochastic Analysis, Random Fields, and Applications V. Progress in Probability 59, 135-174, Birkhäuser Verlag 2007, Basel.
  6. Dynamical percolation on general trees.
    Probability Theory and Related Fields 140(1-2), 129-167.
  7. Hausdorff dimension of the contours of symmetric additive Lévy processes (with Narn-Rueih Shieh and Yimin Xiao). Probability Theory and Related Fields 140(1-2), 169-193.

2007

  1. Hitting probabilities for systems of nonlinear stochastic heat equations with additive noise (with Robert C. Dalang and Eulalia Nualart) ALEA, Vol. III, 231-371.
  2. Normal numbers are normal (Expository).
    Clay Mathematics Institute Annual Report 2006, p. 15 (continued on pp. 27-31).
  3. Images of the Brownian sheet (with Yimin Xiao).
    The Transactions of the AMS, Vol. 359, No. 7, 3125-3151.
  4. Convex rearrangements, generalized Lorenz curves, and correlated Gaussian data (with Y. Davydov, Z. Shi, and R. Zitikis). The J. of Statistical Planning and Inference 137, 915-934.

2006

  1. Sectorial local non-determinism and the geometry of the Brownian sheet (with Dongsheng Wu and Yimin Xiao). Electr. J. Probab., Vol. 11, Paper 33, pp. 817-843.
  2. A note on a.s. finiteness of perpetual integral functionals of diffusions (with Paavo Salminen and Marc Yor), Electr. Comm. Probab., Vol. 11, Paper 11, pp. 108-117.
  3. Exceptional times and invariance for dynamical random walks (with David Asher Levin and Pedro J. Méndez-Hernández). Probab. Th. Rel. Fields 134(3), 383-416.

2005

  1. An extreme-value analysis of the LIL for Brownian motion (with David A. Levin and Zhan Shi) Electr. Comm. Probab., Vol. 10, Paper 20, pp. 196-206.
  2. On dynamical Gaussian random walks (with David Asher Levin and Pedro J. Méndez-Hernández) Ann. Probab. 33(4), 1452-1478.
  3. Lévy processes: capacity, and Hausdorff dimension (With Yimin Xiao)
    Ann. Probab. 33(3), 841-878.
  4. Level crossings of a two-parameter random walk, (With P. Révész, and Z. Shi)
    Stoch. Proc. Their Appl. 115, 359-380.

2004

  1. On the explosion of local times of Brownian sheet along lines, (with P. Révész and Z. Shi)
    Ann. IHP. 40(1), 1-24.
  2. Brownian sheet and quasi-sure analysis,
    Fields Inst. Comm. Vol. 44, 25-47. (Survey)
  3. Recurrent lines in two-parameter isotropic stable stable sheets, (with R. C. Dalang)
    Stoch. Proc. Appl. 114, 81-107.
  4. Additive Lévy processes: Capacity and dimension, (with Yimin Xiao)
    Progress in Probab. Vol. 57, 151-170. (Survey)

2003

  1. Optimal reward on a sparse tree with random edge-weights, (with T. M. Lewis)
    J. of Applied Probab., Vol. 40(4), 926-945.
  2. Measuring the range of an additive Lévy process (or "Local Times of Additive Lévy Processes, II: Existence;" w/ Y. Xiao and Y. Zhong, Ann. Probab. 31(2), 1097-1141.
  3. Intersections of Brownian motions,
    Expos. Math., 21(2), 97-114.
  4. Local times of additive Lévy processes (with Y. Xiao and Y. Zhong)
    Stoch. Proc. Their Appl., 104, 193-216.
  5. Weak unimodality of finite measures, and an application to potential theory of additive Lévy processes. (with Y. Xiao) The Proceedings of the AMS, 131(8), 2611-2616.
  6. The codimension of the zeros of a stable process in random scenery. Sém. de Probab. XXXVII Lecture Notes in Math. 1832, 236-245.

2002

  1. On the most visited sites of symmetric Markov processes. (w/ N. Eisenbaum)
    Stoch. Proc. and Their Appl., 101, 241-256.
  2. Bounds on gambler's ruin probabilities in terms of moments (w/ S. N. Ethier)
    Methodology and Computing in Applied Probab., 4(1), 55-68.
  3. Level sets of additive Lévy processes (w/ Y. Xiao)
    Ann. Probab., 30(1), 62-100.

2000

  1. Images and level sets of additive random walks (w/ Y. Xiao), In: High-dimensional Probab.II, 329-346, Birkhaüser, Boston, (Seattle, 1999; Ed's: E. Giné, D. M. Mason, J. A. Wellner).
  2. Limsup random fractals (w/ Y. Peres and Y. Xiao)
    Elec. J. Probab., 5(4), 1-24.
  3. Sojourn times of Brownian sheet (w/ R. Pemantle)
    Periodica Math. Hung., 41(1-2), 187-194.
  4. On sums of iid random variables indexed by N parameters
    Séminaire de Probab. XXXIV, Lec. Notes in Math., 151-156.
  5. Fast sets and points for fractional Brownian motion (w/ Z. Shi)
    Séminaire de Probab. XXXIV, Lec. Notes in Math., 393-416.
  6. Boundary crossings and the distribution function of the maximum of Brownian sheet (w/ E. Csáki and Z. Shi), Stoch. Proc. Their Appl., 90, 1-18.

1999

  1. Brownian sheet images and Bessel-Riesz capacity
    Trans. Amer. Math. Soc. 351(7), 2607-2622.
  2. Iterated Brownian motion and its intrinsic skeletal structure (w/ T. M. Lewis)
    Progress in Probab.,45, 201-210, Birkhäuser-Verlag, Basel.
  3. Capacity estimates, boundary crossings and the Ornstein-Uhlenbeck process in Wiener space (w/ E. Csáki and Z. Shi), Elec. Comm. Probab., 4(13), 103-109.
  4. Stochastic calculus for Brownian motion on a Brownian fracture (w/ T. M. Lewis)
    Ann. Applied Probab., 9, 629-667.
  5. Brownian sheet and capacity (w/ Z. Shi)
    Ann. Probab., 27, 1135-1159.

1998

  1. A law of the iterated logarithm for stable processes in random scenary (w/ T. M. Lewis)
    Stoch. Proc. Their Appl., 74, 89-121.
  2. Brownian motion in a Brownian crack (w/ K. Burdzy)
    Ann. Applied Probab., 8(3), 708-748.
  3. Chung's law for integrated Brownian motion (w/ Z. Shi)
    Trans. Amer. Math. Soc., 350(10), 4253-4246.
  4. Logarithmic averages of stable random variables are asymptotically normal (w/ I. Berkes and L. Horváth), Stoch. Proc. Their Appl., 77, 35-51.
  5. Gaussian measure of a small ball and capacity in Wiener space (w/ Z. Shi), Asymptotic Methods in Probab. Statist., 453-465, Elsevier Science, Amsterdam, (ed: B. Szyszkowicz).

1997

  1. Some polar sets for the Brownian sheet
    Séminaire de Probab., XXXI, Lec. Notes in Math. 1655, 190-197.
  2. Escape rates for Lévy processes
    Stud. Sci. Math. Hung., 33, 177-183.

1996

  1. The uniform modulus of iterated Brownian motion (w/ T. M. Lewis)
    J. Theoret. Probab., 9(2), 317-333.
  2. Chung's law of the iterated logarithm for iterated Brownian motion (w/ T. M. Lewis)
    Ann. Inst. de l' IHP, 32(3), 349-359.
  3. A strong approximations for logarithmic averages (w/ L. Horváth)
    Stud. Sci. Math. Hungar., 31, 187-196.
  4. On a problem of Erdös and Taylor (w/ T. M. Lewis and Z. Shi)
    Ann. Probab., 23(3), 761-787.
  5. Lévy classes and self-normalization
    Elec. J. Probab., 1(1), 1-18.
  6. Deviation inequalities for continuous martingales
    Stoch. Proc. Their Appl., 65, 17-30.

1995

  1. The gap between the past supremum and the future infimum of a transient Bessel process
    Séminaire de Probab. XXIX, Lec. Notes in Math. 1613, 220-230.
  2. The distribution of bubbles of Brownian sheet
    Ann. Probab.,23(2), 786-805.
  3. The favorite point of a Poisson process (w/ T. M. Lewis)
    Stoch. Proc. Their Appl., 57, 19-38.
  4. Weight functions and pathwise local central limit theorems (w/ L. Horváth)
    Stoch. Proc. Their Appl., 59, 105-123.
  5. The level sets of iterated Brownian motion (w/ K. Burdzy)
    Séminaire de Probab. XXIX, Lec. Notes in Math. 1613, 231-236.

1994

  1. A discrete fractal in Z1
    Proc. Amer. Math. Soc., 120(2), 577-584.
  2. Intersection local time for points of infinite multiplicity. (w/ R. F. Bass and K. Burdzy)
    Ann. Probab., 22(2), 566-626.
  3. Exact rates of convergence to Brownian local times
    Ann. Probab., 22(3), 1295-1330.
  4. Law of the iterated logarithm for local times of the empirical process. (w/ R. F. Bass)
    Ann. Probab., 32(1), 388-399.
  5. On the future infima of some transient processes. (w/ T. M. Lewis and W. V. Li)
    Probab. Theory Related Fields, 99, 337-360.

1993

  1. An embedding of compensated compound Poisson processes with applications to local time
    Ann. Probab., 21(1), 340-361.
  2. Intersection local times and Tanaka formulas, (w/ R. F. Bass)
    Ann. Inst. de l' IHP, 29(3), 419-451.
  3. Strong approximations to Brownian local time (w/ R. F. Bass)
    Sem. in Stoch. Proc., 1992, 43-65, Birkhaüser, (E. Çinlar, K. L. Chung, M. J. Sharp, R. F. Bass and K. Burdzy, Ed.'s).
  4. Rates of convergence to Brownian local time (w/ R. F. Bass)
    Stoch. Proc. Their Appl., 47, 197-213.

1992

  1. Level crossings of empirical processes
    Stoch. Proc. Their Appl., 43, 331-343.
  2. Moment inequalities for functionals of Brownian convex hull
    Ann. Probab., 20(2), 627-630.
  3. Local asymptotic laws for Brownian convex hull
    Probab. Theory Related Fields, 93, 377-392.
  4. Stochastic calculus and continuity of local times of Lévy processes (w/ R. F. Bass)
    Séminaire de Probab. , XXVI, Lec. Notes in Math., 1526, 1-11.
  5. Local times on curves and uniform invariance principles (w/ R. F. Bass)
    Probab. Theory Related Fields, 92, 465-492.
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