Home page of S. Ramasubramanian
Professor
Statistics and Mathematics Unit
Indian Statistical Institute
8th Mile, Mysore Road
Bangalore  560 059
Phone: 08028483002 (Ext.476)
Email: ram at isibang dot ac dot in
Ph.D., Indian Statistical Institute, 1982.
Title of Ph:D: dissertation : Recurrence of Diffusions
Thesis advisor : Professor K.R. Parthasarathy,
Indian Statistical Institute; New Delhi
Research Interests:
Stochastic differential equations, Diffusion processes, Reflected processes,
Skorokhod problem, Insurance models.
Publications
Books
 Lectures on Insurance Models. Texts and Readings in Mathematics,
Vol. 54, Hindustan Book Agency, New Delhi, 2009.

(Edited jointly with M.Delampady and T.Krishnan): Probability and
Statistics. Universities Press, Hyderabad, 2001.
Papers
 (Jointly with Offer Kella): Asymptotic Irrelevance of Initial Conditions for Skorohod Reflection Mapping on the Nonnegative Orthant.
To appear in Mathematics of Operations Research
 A multidimensional ruin problem. To appear in Communications on
Stochastic Analysis, Special Issue in honour of Prof. K.R. Parthasarathy
 Multidimensional insurance model with risk reducing treaty. Stochas
tic Models. 27 (2011) 363  387.
 Multidimensional insurance models. Bulletin of Kerala Mathematics
Association, Special Issue (Guest ed. S.R.S.Varadhan), October 2009,
pp. 129  141.
 (Expository): Large deviations: an introduction to 2007 Abel prize.
Proc. Indian Acad. Sci. (Math. Sci.) 118 (2008) 161  182.
 A dperson differential game with state space constraints. Applied
Mathematics and Optimization 56 (2007) 312  342.
 (Expository): On a Stochastic Model in Insurance. Resonance 11
(2006), no.10, pp. 49  68.
 An insurance network: Nash equilibrium. Insurance: Mathematics
and Economics 38 (2006) 374  390.
 (Expository): Brownian Motion. In Current Trends in Mathematics,
pp. 76  84. Dept. of Mathematics, Madras Christian College, Chennai, 2003.
 (Expository): Some aspects of Large Deviations. In Informal lecture
notes of NBHM sponsored workshop on Partial Differential Equations,
Viscosity Solutions and Applications, pp. 100  121. Indian Institute
of Science, Bangalore, 2003.
 (Expository): Diffusions and the Martingale problem of Stroock and
Varadhan. In Connected at Infinity: a selection of Mathematics by
Indians (ed. R.Bhatia), Texts and Readings in Mathematics, Vol. 25,
pp. 105  129. Hindustan Book Agency, New Delhi, 2003.
 (Jointly with Amites Dasgupta): Transition density of a re
ected symmetric stable Levy process in an orthant. In Probability, Statistics
and their Applications: Papers in honor of Rabi Bhattacharya (ed.
K.B.Athreya, M.Majumdar, M.Puri and E.Waymire), IMS Lecture
Notes  Monograph series, Vol. 41, pp. 117  131. Institute of Mathematical Statistics, Beachwood, Ohio, 2003.
 (Jointly with Amites Dasgupta): On refleected symmetric stable Levy
processes. In Advances in Stochastic Modelling (ed. J.R.Artelejo and
A.Krishnamoorthy) pp. 23  27. Notable Publications Inc., New Jersey, 2002.
 On reflected backward stochastic differential equations. Calcutta Statistical Association Bulletin 52 (2002),
Special 4th Triennial Proceedings Volume (ed. Arijit Chaudhuri and Malay Ghosh) pp. 251  260.
 Reflected backward stochastic differential equations in an orthant.
Proc. Indian Acad. Sci. (Math. Sci.) 112 (2002) 347  360.
 A Skorokhod problem with generalized time and space dependencies.
In Advances in Probability and Stochastic Processes
(ed. A.Krishnamoorthy, N.Raju and V.Ramaswami) pp. 157  166.
Notable Publications Inc., New Jersey, 2001.
 Reflecting Brownian motion in a Lipschitz domain and a conditional
gauge theorem. Sankhya Ser.A 63 (2001) 178  193.
 A Subsidy  Surplus Model and the Skorokhod problem in an Orthant.
Mathematics of Operations Research 25 (2000) 509  538.
 (Expository): On the StroockVaradhan theory of diffusions. Current
Science 78 (2000) 1155  1156.
 (Jointly with S.Balaji): Passage time moments for multidimensional
diffusions. Journal of Applied Probability 37 (2000) 246  251.
 (Jointly with S.Balaji): Asymptotics of reflecting diffusions in an orthant. In Proc. International Conference on Stochastic processes,
Cochin, Dec.1996, (ed. A.Krishnamoorthy) pp. 57  81. Dept. of
Mathematics, Cochin University of Science and Technology, Cochin,
1998.
 (Expository): (Jointly with S.Balaji): Reflecting diffusions in an orthant: an introduction. Differential Equations and Dynamical Systems
6 (1998) 25  36.
 (Jointly with S.Balaji): Reflecting diffusions in the quadrant: recurrence and transience. Differential Equations and Dynamical Systems
6 (1998) 9  24.
 (Jointly with S.Balaji): Recurrence and transience of diffusions in a
half space. Bernoulli 3 (1997) 97  119.
 (Expository): The normal distribution I, II. Resonance 2 (1997), no.6,
pp. 15  24; no.7, pp. 27  37.
 Transition densities of reflecting diffusions. Sankhya Ser.A 58 (1996)
347  381.
 (Expository): Reflecting Diffusions. Current Science 69 (1995) 231  236.
 (Jointly with S.Balaji): Reflecting Brownian motion in a quadrant: a
survey. In Proc. Third Ramanujan Symposium on Stochastic Processes
and their applications, Univ. of Madras, Jan. 1994, pp. 59  70. New
Age International Ltd., New Delhi, 1995.
 On the gauge for the Neumann problem in the half space. Sankhya
Ser.A 56 (1994) 379  384.
 (Jointly with G.Kallianpur, J.Xiong and G.Hardy): The existence and
uniqueness of solutions of nuclear space valued stochastic differential equations driven by Poisson random measures. Stochastics and
Stochastics Reports 50 (1994) 85  122.
 Stochastic solutions of differential equations. In Proc. Mahalanobis
Birth Centenary Symposium on Probability and Statistics, Kerala 1993,
pp. 7  28.
 On the gauge for the third boundary value problem. In Stochastic
Processes: a festschrift in honour of Gopinath Kallianpur (edited by
S.Cambanis, J.K.Ghosh, R.L.Karandikar and P.K.Sen) pp. 285  289.
Springer, New York, 1993.
 Diffusions and the Neumann problem in the half space. Sankhya Ser.A
54 (1992) 351  378.
 Hitting of submanifolds by diffusions. Probability Theory and Related
Fields 78 (1988) 149  163; addendum, ibid 84 (1990) 279.
 (Jointly with R.N.Bhattacharya): On the central limit theorem for
diffusions with almost periodic coeffients. Sankhya Ser.A 50 (1988)
9  25.
 Hitting a boundary point by diffusions in the closed half space. Journal
of Multivariate Analysis 20 (1986) 143  154.
 A characterization of the normal distribution. Sankhya Ser.A 47 (1985)
410  414.
 Recurrence of projections of diffusions. Sankhya Ser.A 45 (1983) 20  31.
 (Jointly with R.N.Bhattacharya): Recurrence and ergodicity of diffusions. Journal of Multivariate Analysis 12 (1982) 95  122.
 An elementary proof of Girsanov's formula. Sankhya Ser.A 41 (1979)
263  270.
Book reviews
 Review of Point Process Theory and Applications: Marked Point and
Piecewise Deterministic Processes by Martin Jacobsen. Sankhya 68
(2006) 359  360.
 Review of Markov Processes from K .Ito's Perspective by Daniel W.
Stroock. Sankhya 67 (2005) 133  136.
 Review of A Concise Introduction to the Theory of Integration by
Daniel W.Stroock. Current Science 78 (2000) 744.
Unpublished expository notes
 Large deviations: introductory notes. Enlarged version of a series of
lectures given at a Summer School on Probability and Applications
held at Kerala School of Mathematics, Kozhikode during May  June
2010.
 Poisson process and insurance: an introduction. Prepared for a series
of lectures given at a Refresher course in Applied Stochastic Processes
sponsored by the Indian Academy of Sciences, Bangalore, held at the
Indian Statistical Institute, New Delhi in Dec. 2005.
 Stochastic differential equations with constant dispersion.
Prepared for
a series of lectures given at a Refresher course in Probability, Stochas
tic Processes and Applications sponsored by the Indian Academy of
Sciences, Bangalore, held at the Dept. of Mathematics, Cochin University of Science and Technology, Kochi in Sept.  Oct., 2005.
 Some connections between S.D.E.'s and P.D.E.'s: an exposition. Prepared for a lecture given at a Discussion Meeting
on Stochastic Differential Equations sponsored by the Indian Academy of Sciences,
Bangalore and the Indian Statistical Institute in June 1991.
Honours, etc.
 Elected a Fellow of the Indian Academy of Sciences, Bangalore with
effect from January 2002.
 Serving on the editorial board of Sankhya since October 1999.
 Served on the editorial board of Resonance during January 2003 to
December 2007.
 Served as a member of the Science Education Panel of the Indian
Academy of Sciences, Bangalore, during 2004  2006.
 Delivered Prof. Wazir Hasan Abdi Memorial Lecture at the Department of Mathematics, Cochin University of Science and Technology,
Kochi in October 2005.
 Delivered Prof. M.N.Gopalan Endowment Lecture at the 22nd Annual Conference of Ramanujan Mathematical Society held at National
Institute of Technology, Surathkal, Karnataka in June 2007.
 Delivered Prof. B.G.Raghavendra Memorial Lecture at the Department of Statistics, University of Mysore in April 2009.
