Reprints of my later papers may be found in ArXiv.org.
- R.F. Bass,
Adding and subtracting jumps from Markov processes,
Trans. Amer. Math. Soc. 255 (1979), 363-376. - R.F. Bass,
Martingales of an independent increment process,
Stoch. Proc. Applic. 9 (1979), 237-244. - R.F. Bass,
Markov processes with Lipschitz semigroups,
Trans. Amer. Math. Soc. 267 (1981), 307-320. - R.F. Bass and M. Cranston,
Brownian motion with lower class moving boundaries which grow faster than t1/2,
Ann. Probability 11 (1983), 34-39. - R.F. Bass and K.B. Erickson,
Hitting time of a moving boundary for a diffusion,
Stoch. Proc. Applic. 14 (1983), 315-325. - R.F. Bass and M. Cranston,
Exit times for symmetric stable processes in Rn,
Ann. Probability 11 (1983), 578-588. - R.F. Bass,
Occupation times for d-dimensional semimartingales,
Seminar on Stochastic Processes, 1982, 51-96, Birkhäuser, Boston, 1983. - R.F. Bass,
Skorokhod imbedding via stochastic integrals,
Séminaire de Probabilités XVII, 221-224, Springer, New York, 1983. - R.F. Bass,
Stochastic integral representations for multiparameter random fields with stationary, independent increments,
Stochastics 11 (1983), 1-17. - R.F. Bass and R. Pyke,
Functional law of the iterated logarithm and uniform central limit theorem for partial-sum processes indexed by sets,
Ann. Probability 12 (1984), 13-34. - R.F. Bass and R. Pyke,
A strong law of large numbers for partial-sum processes indexed by sets,
Ann. Probability 12 (1984), 268-271. - R.F. Bass,
Joint continuity and representations of additive functionals of d-dimensional Brownian motion,
Stoch. Proc. Applic. 17 (1984), 211-228. - R.F. Bass,
Markov processes and convex minorants,
Séminaire de Probabilités XVIII, 29-41, Springer, New York, 1984. - R.F. Bass and R. Pyke,
The existence of set-indexed Lévy processes,
Z. Wahrscheinlichkeitstheorie 66 (1984), 157-172. - R.F. Bass,
Local times for a class of purely discontinuous martingales,
Z. Wahrscheinlichkeitstheorie 67 (1984), 433-459. - R.F. Bass and K.B. Erickson,
Local laws of the iterated logarithm for diffusions,
Ann. Probability 13 (1985), 616-624; 14 (1986), 731. - R.F. Bass and R. Pyke,
The space D(A) and weak convergence for set-indexed processes,
Ann. Probability 13 (1985), 860-884. - R.F. Bass and P.S. Griffin,
The most visited site of Brownian motion and simple random walk,
Z. Wahrscheinlichkeitstheorie 70 (1985), 417-436. - R.F. Bass,
Law of the iterated logarithm for set-indexed partial sum processes with finite variance,
Z. Wahrscheinlichkeitstheorie 70 (1985), 591-608. - R.F. Bass and M. Cranston,
The Malliavin calculus for pure jump processes and applications to local time,
Ann. Probability 14 (1986), 490-532. - R.F. Bass and R. Pyke,
Central limit theorem for D(A)-valued processes,
Stoch. Proc. Applic. 24 (1987), 109-132. - V. Trivedi, I. Moscovice, J. Brooks, and R.F. Bass,
A semi-Markov model for primary health care manpower supply prediction,
Management Sciences 33 (1987), 149-159. - R.F. Bass and E. Pardoux,
Uniqueness for diffusions with piecewise constant coefficients,
Probab. Th. related Fields 76 (1987), 557-572. - R.F. Bass,
Lp inequalities for functionals of Brownian motion,
Séminaire de Probabilités XXI, 206-217, Springer, New York, 1987. - R.F. Bass,
Probability estimates for multiparameter Brownian processes,
Ann. Probability 16 (1988), 251-264. - R.F. Bass,
Occupation time densities for stable-like processes and other pure jump Markov processes,
Stoch. Proc. Applic. 29 (1988), 65-83. - R.F. Bass,
Uniqueness in law for pure jump Markov processes,
Probab. Th. related Fields 79 (1988), 271-287. - M.T. Barlow and R.F. Bass,
The construction of Brownian motion on the Sierpinski carpet,
Ann. de l'Institut H. Poincaré 25 (1989), 225-257. - R.F. Bass,
Using stochastic comparison to estimate Green's functions,
Séminaire de Probabilités XXIII, 421-425, Springer, New York, 1989. - R.F. Bass,
The Dirichlet problem for radially homogeneous elliptic operators,
Trans. Amer. Math. Soc. 320 (1990), 593-614. - M.T. Barlow and R.F. Bass,
Local times for Brownian motion on the Sierpinski carpet,
Probab. Th. related Fields, 85 (1990), 91-104. - R.F. Bass,
A probabilistic approach to the boundedness of singular integral operators,
Séminaire de Probabilités XXIV, 15-40, Springer, New York, 1990. - R. Bañuelos, R.F. Bass, and K. Burdzy,
A representation of local time for Lipschitz surfaces,
Probab. Th. related Fields 84 (1990), 521-547. - R.F. Bass and K. Burdzy,
A probabilistic proof of the boundary Harnack principle,
Seminar on Stochastic Processes, 1989, 1-16, Birkhäuser, Boston, 1990. - R.F. Bass and P. Hsu,
The semimartingale structure of reflecting Brownian motion,
Proc. Amer. Math. Soc., 108 (1990), 1007-1010. - M.T. Barlow, R.F. Bass, and J.D. Sherwood,
Resistance and spectral dimension for Sierpinski carpets,
J. Phys. A: Math. Gen. 23 (1990), L253-L258. - M.T. Barlow and R.F. Bass,
On the resistance of the Sierpinski carpet,
Proc. Royal Soc., Ser. A 431 (1990), 345-360. - R.F. Bass and P. Hsu,
Some potential theory for reflecting Brownian motion in Hölder and Lipschitz domains,
Ann. Probability, 19 (1991), 486-508. - R.F. Bass and K. Burdzy,
A boundary Harnack principle for twisted Hölder domains,
Annals of Math., 134 (1991), 253-276. - Bañuelos, R.F. Bass, and K. Burdzy,
Hölder domains and the boundary Harnack principle,
Duke Math. J., 64 (1991), 195-200. - R.F. Bass and K. Burdzy,
Lifetimes of conditioned diffusions,
Probab. Th. related Fields, 91 (1992) 405-444. - R.F. Bass,
A centred norm inequality for singular integral operators,
Math. Proc. Cambridge Phil. Soc., 112 (1992) 369-383. - M.T. Barlow and R.F. Bass,
Transition densities for Brownian motion on the Sierpinski carpet,
Probab. Th. related Fields, 91 (1992) 307-330. - R.F. Bass and D. Khoshnevisan,
Stochastic calculus and the continuity of local times of Lévy processes,
Séminaire de Probabilités, 1-10, Springer, New York, 1992. - R.F. Bass and D. Khoshnevisan,
Local times on curves and uniform invariance principles,
Probab. Th. related Fields, 92 (1992) 465-492. - R.F. Bass and K. Burdzy,
The Martin boundary in non-Lipschitz domains,
Trans. Amer. Math. Soc., 337 (1993) 361-378. - R.F. Bass and D. Khoshnevisan,
Intersection local times and Tanaka formulas,
Ann. de l'Institut H. Poincaré, 29 (1993) 419-451. - R.F. Bass and D. Khoshnevisan,
Strong approximations to Brownian local time,
Seminar on Stochastic Processes, 1992, 43-65, Birkhäuser, Boston, 1993. - R.F. Bass and K. Burdzy, (managing editors)
Seminar on Stochastic Processes 1992,
Birkhäuser, Boston, 1993. - R.F. Bass and D. Khoshnevisan,
Rates of convergence to Brownian local time,
Stoch. Proc. Appl., 47 (1993) 197-213. - R.F. Bass and K. Burdzy,
On domain monotonicity of the Neumann heat kernel,
J. Functional Anal., 116 (1993) 215-224. - M.T. Barlow and R.F. Bass,
Coupling and Harnack inequalities for Sierpinski carpets,
Bull. Amer. Math. Soc., 29 (1993) 208-212. - R.F. Bass and K. Burdzy,
The boundary Harnack principle for non-divergence form elliptic operators,
J.~Lon. Math. Soc., 50(1994) 157-169. - R.F. Bass, K. Burdzy, and D. Khoshnevisan,
Intersection local times for points of infinite multiplicity,
Ann. Probab., 22 (1994) 566-625. - R.F. Bass,
Probabilistic Techniques in Analysis,
New York, Springer, 1995. - R.F. Bass and D. Khoshnevisan,
Laws of the iterated logarithm for local times of the empirical process,
Ann. Probab., 23 (1995) 388-399. - R.F. Bass and K. Burdzy,
Conditioned Brownian motion in planar domains,
Probab. Theory rel. Fields, 101 (1995) 479-493. - R.F. Bass,
Brownian motion, heat kernels, and harmonic functions,
Proc. International Congress of Mathematicians 1994, Vol. 2, 980-985, Birkhäuser, Basel, 1995. - R.F. Bass,
The Doob-Meyer decomposition revisited,
Can. Math. Bull., 39 (1996) 138-150. - R.F. Bass and K. Burdzy,
A critical case for Brownian slow points,
Probab. Th. rel. Fields, 105 (1996) 85-108. - R.F. Bass and K. Burdzy,
Eigenvalue expansions for Brownian motion with an application to occupation times,
Electronic J. Prob., 1 (1996) Paper no. 3, 1-19. - R.F. Bass,
Uniqueness for the Skorokhod equation with normal reflection in Lipschitz domains,
Electronic J. Prob, 1 (1996) Paper no. 11, 1-29. - R.F. Bass,
Diffusions on the Sierpinski carpet,
Trends in Probability and Related Analysis, 1-34, World Scientific, Singapore, 1997. - R.F. Bass,
A review of Ross G. Pinsky Positive harmonic functions and diffusion: an integrated analytic and probabilistic approach,
Ann. Probab., 25 (1997) 1532-1535. - R.F. Bass,
Diffusions and Elliptic Operators, New York,
Springer, 1997. - M.T. Barlow, R.F. Bass, and K. Burdzy,
Positivity of Brownian transition densities,
Electronic Comm. Prob., 2 (1997) 43-51. - R.F. Bass and K. Burdzy,
Cutting Brownian paths,
Mem. Amer. Math. Soc., 137 (1999) Number 657, 99 pages. - M.T. Barlow and R.F. Bass,
Brownian motion and harmonic analysis on Sierpinski carpets,
Canad. J. Math. 51, (1999), 673-744. - M.T. Barlow and R.F. Bass,
Random walks on graphical Sierpinski carpets,
In: Random walks and discrete potential theory, 26-55, Cambridge, Cambridge Univ. Press, 1999. - R.F. Bass and K. Burdzy,
Stochastic bifurcation models,
Ann. Prob., 27 (1999) 50-108. - R.F. Bass,
A review of Mark Yor: Some aspects of Brownian motion, Part II: some recent martingale problems,
Metrika 49 (1999) 164-165. - R.F. Bass and E. Hsu,
Pathwise uniqueness for reflecting Brownian motion in Euclidean domains,
Probab.Th. rel. Fields 117 (2000) 183-200.
See "On pathwise uniqueness for reflecting Brownian motion in C1+γ domains" for further information. - R.F. Bass, N. Eisenbaum, and Z. Shi,
The most visited sites for symmetric stable processes,
Probab. Th. rel. Fields 116 (2000) 391-404. - M.T. Barlow, R.F. Bass, and C. Gui,
The Liouville property and a conjecture of De Giorgi,
Comm. Pure Appl. Math. 53 (2000) 1007-1038. - R.F. Bass and T. Kumagai,
Laws of the iterated logarithm for some symmetric diffusion processes,
Osaka J. Math. 37 (2000) 625-650. - R.F. Bass and K. Burdzy,
Fiber Brownian motion and the ``hot spots'' problem,
Duke Math. J. 105 (2000) 25-58. - M.T. Barlow and R.F. Bass,
Divergence form operators on fractal-like domains,
J. Functional Anal. 175 (2000) 214-247. - R.F. Bass and E. Perkins,
On the martingale problem for super-Brownian motion,
Séminaire de Probabilités XXXV, 195-201, Springer, New York, 2001. - R.F. Bass and K. Burdzy,
The supremum of Brownian local times on Hölder curves,
Ann. I.H. Poincaré 37 (2001) 627-642; 38 (2002) 799-800. - R.F. Bass and Z.-Q. Chen,
Stochastic differential equations for Dirichlet processes,
Probab. Th. rel. Fields 121, (2001) 422-446. - R.F. Bass,
A uniqueness result for harmonic functions,
Proc. Amer. Math. Soc. 130 (2002) 1711-1716. - R.F. Bass, B. Hambly, and T.J. Lyons,
Extending the Wong-Zakai theorem to reversible Markov processes,
J. European Math. Soc. 4 (2002) 237-269. - R.F. Bass and D.A. Levin,
Harnack inequalities for jump processes,
Potential Anal. 17 (2002) 375-388. - R.F. Bass and T. Kumagai,
Laws of the iterated logarithm for the range of random walks in two and three dimensions,
Ann. Probab. 30 (2002) 1369-1396. - R.F. Bass,
On Aronson's upper bounds for heat kernels,
Bull. London Math. Soc. 34 (2002) 415-419. - S. Athreya, M.T. Barlow, R.F. Bass, and E. Perkins,
Degenerate stochastic differential equations and super-Markov chains,
Probab. Th. rel. Fields 123 (2002) 484-520. - R.F. Bass and D.A. Levin,
Transition probabilities for symmetric jump processes,
Trans. Amer. Math. Soc. 354 (2002) 2933-2953. - R.F. Bass,
Stochastic differential equations driven by symmetric stable processes,
Séminaire de Probabilités XXXVI, 302-313, Springer, New York, 2003.
See also the paper "Stochastic differential equations driven by stable processes for which pathwise uniqueness fails" for further information. - R.F. Bass and Z.-Q. Chen,
Brownian motion with singular drift,
Ann. Probab. 31 (2003), 791-817. - R.F. Bass and E. Perkins,
Degenerate stochastic differential equations with Hölder continuous coefficients and super-Markov chains,
Trans. Amer. Math. Soc. 355 (2003) 373-405. - R.F. Bass and H. Farnsworth,
The term structure with semi-credible targeting,
J. Finance 58 (2003) 839-866. - R.F. Bass and D. You,
A Fatou theorem for α-harmonic functions,
Bull. Sciences Math. 127 (2003) 635-648. - M.T. Barlow and R.F. Bass,
Stability of parabolic Harnack inequalities,
Trans. Amer. Math. Soc. 356 (2004) 1501-1533. - R.F. Bass, K. Burdzy, and Z.-Q. Chen,
Stochastic differential equations driven by stable processes for which pathwise uniqueness fails,
Stoch. Proc. Applic. 111 (2004) 1-15. - R.F. Bass, J. Horák, and P.J. McKenna,
On the lift-off constant for elastically supported plates,
Proc. Amer. Math. Soc. 132 (2004) 2951-2958. - R.F. Bass and X. Chen,
Self-intersection local time: critical exponent, large deviations, and laws of the iterated logarithm,
Ann. Probability 32 (2004) 3221-3247. - R.F. Bass, and K. Gröchenig,
Random sampling of multivariate trigonometric polynomials,
SIAM J. of Math. Anal. 36 (2004) 773-795. - R.F. Bass,
Stochastic differential equations with jumps,
Prob. Surveys, 1 (2004) 1-19. - R.F. Bass and E. Perkins,
Countable systems of degenerate stochastic differential equations with applications to super-Markov chains,
Electron. J. Probab. 9 (2004) 634-673. - R.F. Bass, K. Burdzy, and Z.-Q. Chen,
Uniqueness of reflecting Brownian motion in lip domains,
Ann. de l'Institut H. Poincaré 41, (2005) 197-235. - R.F. Bass and M. Kassmann,
Harnack inequalities for non-local operators of variable order,
Trans. Amer. Math. Soc. 357 (2005) 837-850. - S. Athreya, R.F. Bass, and E. Perkins,
Hölder norm estimates for elliptic operators on finite and infinite dimensional spaces,
Trans. Amer. Math. Soc. 357 (2005) 5001-5029. - R.F. Bass, X. Chen, and J. Rosen,
Large deviations for renormalized self-intersection local times of stable processes,
Ann. Prob. 33 (2005) 984-1013. - R.F. Bass and M. Kassmann,
Hölder continuity of harmonic functions with respect to operators of variable order,
Comm. PDE 30 (2005) 1249-1259. - R.F. Bass and J. Rosen,
An almost sure invariance principle for the range of planar random walks,
Ann. Probab. 33 (2005) 1856-1885. - R.F. Bass and Z.-Q. Chen,
One-dimensional stochastic differential equations with singular and degenerate coefficients,
Sankhya 67 (2005) 19-45. - R.F. Bass and J. Rosen,
An almost sure invariance principle for renormalized intersection local times,
Electron. J. Probab. 10 (2005) 124-164. - R.F. Bass and D. You,
A Fatou theorem for α-harmonic functions in Lipschitz domains,
Prob. Th. rel. Fields 133 (2005) 391-408. - J. Vadiveloo and R.F. Bass,
Actuarial analysis of different interpretations of SOP-03-01,
Fin. Reporter of Soc. of Actuaries 60, March, 2005, 1-5. - R.F. Bass and Z.-Q. Chen,
Systems of equations driven by stable processes,
Probab. Th. rel. Fields 134 (2006) 175-214. - M.T. Barlow, R.F. Bass, and T. Kumagai,
Stability of parabolic Harnack inequalities for metric measure spaces,
J. Math. Soc. Japan 58 (2006) 485-519. - S.R. Athreya, R.F. Bass, M. Gordina, and E.A. Perkins,
Infinite dimensional stochastic differential equations of Ornstein-Uhlenbeck type,
Stoch. Proc. Applic. 116 (2006) 381-406. - R.F. Bass, X. Chen, and J. Rosen,
Moderate deviations and laws of the iterated logarithm for the renormalized self-intersection local times of planar random walks,
Electron. J. Probab. 11 (2006) 993-1030. - R.F. Bass and K. Burdzy,
Pathwise uniqueness for two dimensional reflecting Brownian motion in Lipschitz domains,
Electron. Comm. Probab. 11 (2006) 178-181. - R.F. Bass and A. Lavrentiev,
The submartingale problem for a class of degenerate elliptic operators,
Probab. Th. rel. Fields 139, (2007) 415-449. - R.F. Bass, K. Burdzy, and Z.-Q. Chen,
Pathwise uniqueness for a degenerate stochastic differential equation,
Ann. Probab. 35 (2007) 2385-2418. - R.F. Bass and J. Rosen,
Frequent points for random walks in two dimensions,
Electron. J. Probab. 12 (2007) 1-46. - R.F. Bass, K. Burdzy, and Z.-Q. Chen,
On the Robin problem in fractal domains,
Proc. London Math. Soc. 96 (2008) 273-311. - R.F. Bass and T. Kumagai,
Symmetric Markov chains on Zd with unbounded range,
Trans. Amer. Math. Soc. 360 (2008) 2041-2075. - R.F. Bass and K. Burdzy,
On pathwise uniqueness for reflecting Brownian motion in C1+γ domains,
Ann. Probab. 36 (2008) 2311-2331. - R.F. Bass and E.A. Perkins,
Degenerate stochastic differential equations arising from catalytic branching networks,
Electron. J. Probab. 13 (2008) 1808-1885. - R.F. Bass, X. Chen, and J. Rosen,
Moderate deviations for the range of planar random walks,
Memoirs Amer. Math. Soc. 198 (2009) Number 929, 82 pages. - M.T. Barlow, R.F. Bass, Z.-Q. Chen, and M. Kassmann,
Non-local Dirichlet forms and symmetric jump processes,
Trans. Amer. Math. Soc. 361 (2009) 1963-1999. - M.T. Barlow, R.F. Bass, and T. Kumagai,
Parabolic Harnack inequality and heat kernel estimates for random walks with long range jumps,
Math. Z. 261 (2009) 297-320. - R.F. Bass and H. Tang,
The martingale problem for a class of stable-like processes,
Stoch. Proc. Applic. 119 (2009) 1144-1167. - R.F. Bass,
Regularity results for stable-like operators,
J. Functional Anal. 257 (2009) 2693-2722. - R.F. Bass, X. Chen, and J. Rosen,
Large deviations for Riesz potentials of additive processes,
Ann. de l'Institut H. Poincaré 45 (2009) 626-666. - R.F. Bass and E.A. Perkins,
A new technique for proving uniqueness for martingale problems,
From Probability to Geometry (I): Volume in Honor of the 60th Birthday of Jean-Michel Bismut, 47-53.
Société Mathématique de France, Paris, 2009. - R.F. Bass, K. Burdzy, Z.-Q. Chen, and M. Hairer,
Stationary distributions for diffusions with inert drift,
Probab. Th. rel. Fields 146 (2010) 1-47. - R.F. Bass,
The measurability of hitting times ,
Electron. Comm. Probab. 15 (2010) 99-105; 16 (2011) 189-191.
There is a correction to the paper on ArXiv.org. - M.T. Barlow, R.F. Bass, T. Kumagai, and A. Teplyaev,
Uniqueness for Brownian motion on Sierpinski carpets,
J. Europ. Math. Soc. 12 (2010) 655-701. - R.F. Bass and K. Gröchenig,
Random sampling of band-limited functions,
Israel J. Math. 177 (2010) 1-28. - R.F. Bass, T. Kumagai, and T. Uemura,
Convergence of symmetric Markov chains on Zd,
Probab. Th. rel. Fields 148 (2010) 107-140. - R.F. Bass, M. Kassmann, and T. Kumagai,
Symmetric jump processes: localization, heat kernels, and convergence,
Ann. de l'Institut H. Poincaré 46 (2010) 59-71. - R.F. Bass and Z.-Q. Chen,
Regularity of harmonic functions for a class of singular stable-like processes,
Math. Z. 266 (2010) 489-503. - R.F. Bass, Stochastic Processes,
Cambridge University Press, Cambridge, 2011. - R.F. Bass, Real Analysis for Graduate Students: Measure and Integration Theory,
CreateSpace, Charleston, 2011. xiv+194 pp. - R.F. Bass and E.A. Perkins,
On uniqueness in law for parabolic SPDEs and infinite dimensional SDEs.
Electronic J. Prob., 17 (2012) Paper no. 36, 1-54. - R.F. Bass, and M. Gordina,
Harnack inequalities in infinite dimensions,
J. Functional Anal., 263 (2012) 3707-3740. - R.F. Bass, Real Analysis for Graduate Students, Second Edition,
CreateSpace, Charleston, 2013. - R.F. Bass,
A stability theorem for elliptic Harnack inequalities ,
J. Europ. Math. Soc., 17 (2013) 856-876. - R.F. Bass, and H. Ren,
Meyers inequality and strong stability for stable-like operators,
J. Functional Anal., 265 (2013) 28-48.
There is a correction to this paper on ArXiv.org. - R.F. Bass, and K. Gröchenig,
Relevant sampling of band-limited functions,
Illinois J. Math., 57 (2013) 43-58. - R.F. Bass,
A stochastic differential equation with a sticky point,
Electron. J. Probab., 19 (2014) Article 32, 1-22. - R.F. Bass, Real Analysis for Graduate Students, Version 2.1,
CreateSpace, Charleston, 2014. - R.F. Bass, Real Analysis for Graduate Students, Version 3.1,
2016. - R.F. Bass, Real Analysis for Graduate Students, Version 4.1,
2020. - R.F. Bass, Real Analysis for Graduate Students, Version 4.2,
2020. - R.F. Bass, Real Analysis for Graduate Students, Version 4.3,
2022. - R.F. Bass,
The rate of escape of the most visited site of Brownian motion,
Electron. J. Probab., 28 (2023) Article 20, 1-12. - R.F. Bass and K. Burdzy, The supremum of Brownian local times on H\"older curves revisited,
Ann. Inst. H. Poincaré to appear. - R.F. Bass and K. Burdzy, Pathwise non-uniqueness for Brownian motion in a quadrant with oblique reflection,
preprint. - R.F. Bass and K. Burdzy, Uniqueness for the Skorokhod problem in an orthant: critical cases ,
preprint.
For related results see Two results from Mandelbaum's paper: "The dynamic complementarity problem" on ArXiv.org. - R.F. Bass, Real Analysis for Graduate Students, Version 5.0, 2024.