Branching processes & related large deviations
Jiang, X. and Vidyashankar, A.N. (2025): Ancestral inference and learning for branching processes in random environments. https://arxiv.org/pdf/2501.16526
Francisci, G. and Vidyashankar, A.N. (2024): Functional limit laws for the intensity measure of point processes and their applications. https://arxiv.org/pdf/2402.05087.pdf
Collamore, J.F., de Silva, H., and Vidyashankar, A.N. (2022): Sharp probability tail estimates for portfolio credit risk. Risks, 10, (12), 239.
Francisci, G. and Vidyashankar, A.N. (2022): Branching processes in random environments with thresholds, arXiv: 2207.02287[math.PR], To Appear, The Advances in Applied Probability.
Vidyashankar, A.N. and Collamore, J.F. (2021): Rare event analysis for minimum Hellinger distance estimators via large deviation theory, Entropy, Volume 23, Issue 4.
Kuelbs, J. and Vidyashankar, A.N. (2011): Weak convergence results for multiple generations of branching processes, Journal of Theoretical Probability, 24, pp. 376-396.
Kuelbs, J. and Vidyashankar, A.N. (2009): Functional limit laws of Strassen and Wichura type for Multiple Generations of Branching Processes, High Dimensional Probability-The Luminy Volume, 5, pp. 131-152.
Ney, P.E. and Vidyashankar, A.N. (2008): Conditional limit laws and inference for the generation sizes of branching processes, Markov Processes and Related Topics: A Festschrift for Thomas G. Kurtz, IMS Lecture Note Series, (Ethier, Feng, eds.), pp. 17-30.
Ney, P.E. and Vidyashankar, A.N. (2004): Local limit theory and large deviations for supercritical branching processes, Annals of Applied Probability, 3, pp. 1135-1166.
Ney, P.E. and Vidyashankar, A.N. (2003): Harmonic moments and large deviation rates for supercritical branching processes, Annals of Applied Probability, 2, pp. 475-489.
Athreya, K.B. and Vidyashankar, A.N. (1997): Large devia-tion rates for supercritical and critical branching processes, in Classical and Modern Branching Processes (Athreya, K.B.,Jagers, P. eds.), IMA Vol. Math. Appl., 84, Springer, New York, pp. 1-18.
Athreya, K.B. and Vidyashankar, A.N. (1995): Large deviation rates for branching processes-II, the multitype case, Annals of Applied Probability, 5, pp. 566-576.
Athreya, K.B. and Vidyashankar, A.N. (1993): Large deviation results for branching processes, Stochastic Processes, A festschrift in honor of Gopinath Kallianpur, (Cambanis, S., Ghosh, J.K., Karandikar, R.L. and Sen, P.K. eds.), pp. 7-12, Springer, New York.
Stochastic fixed point equations
Collamore, J.F., Diao, G., and Vidyashankar, A.N. (2014): Rare event simulation for processes generated via Stochastic Fixed Point Equations, Annals of Applied Probability, 24, pp. 2143-2175.
Vidyashankar, A.N. and Xu, J. (2013): Adaptive nested rare event simulation algorithms, Proceedings of the Winter Simulation Conference, Washington D.C., December 2013, pp. 736-744.
Collamore, J.F., Vidyashankar, A.N. and Xu, J. (2013): Rare event simulation for stochastic fixed point equations related to the smoothing transform, Proceedings of the Winter Simulation Conference, Washington D.C., December 2013, pp. 555-563.
Collamore, J.F. and Vidyashankar, A.N. (2013): Large deviation tail estimates and related limit laws for stochastic fixed point equations, in Random Matrices and Iterated Random Functions (Alsmeyer, G., Lowe, M. eds.), Springer, pp. 91-118.
Collamore, J.F. and Vidyashankar, A.N. (2013): Tail estimates for stochastic fixed point equations via nonlinear renewal theory, Stochastic Processes and their Applications, 123, pp. 3378-3429.
Urn models
Aletti, G., Ghigilietti, A., and Vidyashankar, A.N. (2018): Dynamics of an adaptive randomly reinforced urn, Bernoulli, 24, pp. 2204-2255.
Ghiglietti, A., Vidyashankar, A.N., Rosenberger, W. (2017): Central limit theorem for an adaptive randomly reinforced urn model, The Annals of Applied Probability, 27, pp. 2956-3003.