Research Interests
SDE with Levy noise, Markovian switching and delays, McKean--Vlasov SDE, interacting particle system, financial mathematics, stochastic gradient method.
BioSketch
Research
Milstein Scheme for Stochastic Differential Equation with Markovian Switching and L\'evy Noise
2024
D. Vashistha and C. Kumar | Elsevier
Journal: Journal of Mathematical Analysis and Applications Pages: 128175 , Volumes: 536 ,
An explicit Milstein-type scheme for interacting particle systems and McKean-Vlasov SDEs with common noise and non-differentiable drift coefficients
2024
S. Biswas, C. Kumar, Neelima, G. dos Reis and C. Reisinger | Institute of Mathematical Statistics
Journal: Annals of Applied Probability Pages: 2326--2363 , Volumes: 34 (2) ,
Tamed Explicit Scheme of Order 2.0 for Stochastic Differential Equations with Super-linear Drift and Diffusion Coefficients
2023
T. Kumar and C. Kumar | preprint
Journal: preprint Pages: 1-50 ,
On Ito-Taylor expansion for stochastic differential equations with Markovian switching and its application in gamma-order scheme,
2022
T. Kumar and C. Kumar | Preprint
Journal: Preprint Pages: 1-53 ,
Well-posedness and tamed schemes for McKean{Vlasov Equations with Common Noise
2022
C. Kumar, Neelima, C. Reisinger and W. Stockinger | Institute of Mathematical Statistics
Journal: Annals of Applied Probability Pages: 3283--3330 , Volumes: 32(5) ,
On Explicit Milstein-type Scheme for Mckean--Vlasov Stochastic Differential Equations with Super-linear Drift Coefficient
2021
C. Kumar and Neelima | Institute of Mathematical Statistics and Bernoulli Society
Journal: Electronic Journal of Probability Pages: 1-32 , Volumes: 26 (111) ,
A Note on Explicit Milstein-Type Scheme for Stochastic Differential Equation with Markovian Switching
2021
C. Kumar and T. Kumar | Elsevier
Journal: Journal of Computational and Applied Mathematics Pages: 113594 , Volumes: 395 ,
On Milstein-type schemes of SDE driven by Levy noise with superlinear diffusion coeffcients
2021
C. Kumar | American Institute of Mathematical Sciences
Journal: Discrete and Continuous Dynamical Systems - Series B Pages: 1405-1446 , Volumes: 26(3) ,
Well-posedness and tamed Euler schemes for McKean--Vlasov equations driven by Levy noise
2020
Neelima, S. Biswas, C. Kumar, G. dos Reis and C. Reisinger | Preprint
Journal: Preprint Pages: 1-33 ,
On explicit tamed Milstein-type scheme for stochastic differential equation with Markovian switching
2020
C. Kumar and T. Kumar | Elsevier
Journal: Journal of Computational and Applied Mathematics Pages: 112917 , Volumes: 377 ,
On Milstein approximations with varying coefficients: the case of super-linear diffusion coefficients
2019
C. Kumar and S. Sabanis | Springer Science+Business Media
Journal: BIT Numerical Mathematics Pages: 929-968 , Volumes: 59(4) ,
On fixed gain recursive estimators with discontinuity in the parameters
2019
Huy N. Chau, C. Kumar, M. Rasonyi and S. Sabanis | EDP Sciences
Journal: ESAIM: Probability and Statistics Pages: 217-244 , Volumes: 23 ,
On Explicit Approximations for Levy Driven SDEs with Superlinear Diffusion Coefficients
2017
C. Kumar and S. Sabanis | Institute of Mathematical Statistics and Bernoulli Society
Journal: Electronic Journal of Probability Pages: 1-19 , Volumes: 22 ,
On tamed Milstein scheme of SDEs driven by Levy noise
2017
C. Kumar and S. Sabanis | American Institute of Mathematical Sciences
Journal: Discrete and Continuous Dynamical Systems-Series B Pages: 421-463 , Volumes: 22(2) ,
On tamed Euler approximations of SDEs driven by Levy noise with application to delay equations
2016
K. Dareiotis, C. Kumar and S. Sabanis | Society for Industrial and Applied Mathematics
Journal: SIAM Journal on Numerical Analysis Pages: 1840-1872 , Volumes: 54(3) ,
Strong convergence of Euler approximations of stochastic differential equations with delay under local Lipschitz condition
2014
C. Kumar and S. Sabanis | Taylor & Francis
Journal: Stochastic Analysis and Applications Pages: 207-228 , Volumes: 32(2) ,
Honors And Awards
Students
Miscellaneous
Bochum, Germany
2015-07-08
Explicit numerical schemes of SDEs driven by Levy noise with super-linear coeffcients and their applications to delay equations, Ruhr-Universitat Bochum, Germany, 8 July 2015.
Oxford, United Kingdom
2015-02-26
On tamed Milstein scheme of SDEs driven by Levy noise, Oxford's SIAM Conference, Mathematical Institute, University of Oxford, UK, 26 February 2015 (contributed talk).
Oxford, United Kingdom
2014-05-28
On tamed Euler schemes of SDEs driven by Levy noise with application to delay equations, 3rd SIAM National Student Chapter Conference, Mathematical Institute, University of Oxford, UK, 28 May 2014 (poster presentation).
Edinburgh, United Kingdom
2013-12-06
Numerical approximations of SDEs, Annual meeting of the probability groups of the Maxwell Institute for the Mathematical Sciences, International Centre for Mathematical Sciences, Edinburgh, UK, 6 December 2013 (invited talk)
Vienna, Austria
2013-09-03
Numerical techniques for SDEs with random coefficients and jumps, Summer School on Numerical Methods for Stochastic Differential Equations, Vienna University of Technology, Vienna, Austria, 2-4 September 2013 (contributed talk).
Tamed Euler schemes of SDEs (SDDEs) driven by Levy noise, Indian Statistical Institute, Delhi Center, India, 5 September 2015 (invited talk).
I have organized a session jointly with Goncalo Dos Reis on Numerical methods for non linear McKean-Vlasov SDEs, 9th International Colloquium on Backward Stochastic Differential Equations and Mean Field Systems (BSDE2022), 27 June-01 July 2022
Thiruvananthapuram, India
2023-03-09
Well-posedness and tamed schemes for distribution dependent SDEs, National Conference on Applied Mathematics and Numerics, 8-10 March 2023, Mar Ivanios College (Autonomous) and Indian Institute of Space Science and Technology (Invited).
Trivandrum, India
2019-06-07
On Milstein approximations with varying coefficients: the case of super-linear diffusion coefficients, National Conference on Stochastic Differential Equations and Applications, IIST Trivandrum, 6-7 June, 2019 (invited speaker).
Bangalore, India
2018-12-08
Towards higher order explicit scheme for SDE with super-linear coefficients, Lectures in Probability and Stochastic Processes XIII, Indian Statistical Institute Bangalore, 07 - 11 December, 2018 (invited talk).
Barcelona, Spain
2016-06-01
Explicit Milstein schemes of SDEs: the case of super-linear coefficients, 3rd Barcelona Summer School on Stochastic Analysis, Centre de Recerca Matematica, Bellaterra, 27 June -1 July 2016
