· “On the relative value iteration with a risk-sensitive criterion,” Ari Arapostathis and Vivek S. Borkar, arXiv: 1912.08758.

· “Optimal sensor scheduling under intermittent observations subject to network dynamics,” Carroll Johnson, Hassan Hmedi, and Ari Arapostathis arXiv: 1912.07107.

· “On the policy improvement algorirhm for ergodic risk-sensitive control,” Ari Arapostathis, Anup Biswas, and Somnath Pradhan arXiv: 1912.04568.

· “Risk-sensitive control for a class of diffusions with jumps,” Ari Arapostathis and Anup Biswas, arXiv: 1910.05004.

· “Exponential ergodicity and steady-state approximations for a class of Markov processes under fast regime switching,” Ari Arapostathis, Guodong Pang, and Yi Zheng, arXiv: 1909.05733.

· “Open Problem–Convergence and asymptotic optimality of the relative value iteration in ergodic control,” Ari Arapostathis, *Stochastic Systems ***9 **(2019), no. 3, online. **DOI:** 10.1287/stsy.2019.0040.

· “Optimal scheduling of critically loaded multiclass GI/M/n+M queues in an alternating renewal environment,” Ari Arapostathis, Guodong Pang, and Yi Zheng, arXiv: 1908.06329.

· “Ergodic control of diffusions with compound Poisson jumps under a general structural hypothesis,” Ari Arapostathis, Guodong Pang, and Yi Zheng, arXiv: 1908.01068.

· “Rate of convergence in Wasserstein distance of piecewise-linear Lévy-driven SDEs,” Ari Arapostathis, Guodong Pang, and Nikola Sandrić, arXiv: 1907.05250.

· “On uniform stability of certain parallel server networks with no abandonment in the Halfin-Whitt regime,” Hassan Hmedi, Ari Arapostathis, and Guodong Pang, arXiv: 1907.04793.

· “On uniqueness of solutions to viscous HJB equations with a subquadratic nonlinearity in the gradient,” Ari Arapostathis, Anup Biswas, and Luis Caffarelli, *Communications in Partial Differential Equations ***44** (2019), no. 12, 1466-1480. **DOI:**10.1080/03605302.2019.1645697. available at arXiv: 1906.11733.

· “'Controlled' versions of the Collatz-Wielandt and Donsker-Varadhan formulae,” Ari Arapostathis and Vivek S. Borkar, arXiv: 1903.10714.

· “A variational characterization of the risk-sensitive average reward for controlled diffusion on R^d” Ari Arapostathis, Anup Biswas, Vivek S. Borkar, and K. Suresh Kumar, arXiv: 1903.08346.

· “Average cost optimal control under weak hypotheses: Relative value iterations,” Ari Arapostathis and Vivek S. Borkar, arXiv: 1902.01048.

· “On uniform exponential ergodicity of Markovian multiclass many-server queues in the Halfin-Whitt regime,” Ari Arapostathis, Hassan Hmedi, and Guodong Pang, arXiv: 1812.03528.

· “A variational formula for risk-sensitive control of diffusions in R^d,” Ari Arapostathis and Anup Biswas, *SIAM Journal on Control and Optimization *(to appear), available in arXiv: 1810.01180.

· “Uniform polynomial rates of convergence for a class of Lévy-driven controlled SDEs arising in multiclass many-server queues,” Ari Arapostathis, Hassan Hmedi, Guodong Pang, and Nikola Sandrić, in Yin G., Zhang Q. (eds) Modeling, Stochastic Control, Optimization, and Applications. The IMA Volumes in Mathematics and its Applications, vol. 164, pp. 1-20, Springer, Cham, 2019. **DOI:** 10.1007/978-3-030-25498-8_1

· “Optimal control of Markov-modulated multiclass many-server queues,” Ari Arapostathis, Anirban Das, Guodong Pang, and Yi Zheng, *Stochastic Systems ***9 **(2019), no. 2, 155-181. **DOI:** 10.1287/stsy.2019.0029.

· “Ergodic control of a class of jump diffusions with finite Lévy measures and rough kernels,” Ari Arapostathis, Luis Caffarelli, Guodong Pang, and Yi Zheng, *SIAM Journal on Control and Optimization* **57** (2019), no. 2, 1516-1540. **DOI: **10.1137/18M1166717.

· “Strict monotonicity of principal eigenvalues of elliptic operators in R^d and risk-sensitive control,” Ari Arapostathis, Anup Biswas, and Subhamay Saha,* Journal des Mathématiques Pures et Appliquées* **124** (2019), 169-219. **DOI:** 10.1016/j.matpur.2018.05.008.

· “Certain Liouville properties of eigenfunctions of elliptic operators,” Ari Arapostathis, Anup Biswas, and Debdip Ganguly, *Transactions of the American Mathematical Society ***371** (2019), no. 6, 4377-4409. **DOI:** 10.1090/tran/7694.

· “Ergodicity of Lévy-driven SDEs arising from multiclass many-server queues,” Ari Arapostathis, Guodong Pang, and Nikola Sandrić, *Annals of Applied Probability* **29** (2019), no. 2, 1070-1126. **DOI: **10.1214/18-AAP1430.

· “Infinite horizon asymptotic average optimality for large-scale parallel server networks,” Ari Arapostathis and Guodong Pang, *Stochastic Processes and Their Applications* **129** (2019), no. 1, 283-322. **DOI:** 10.1016/j.spa.2018.03.005.

· “Augmenting Max-Weight with explicit learning for wireless scheduling with switching costs,” Subhashini Krishnasamy, Akhil P T, Ari Arapostathis, Rajesh Sundaresan, and Sanjay Shakkottai, *IEEE/ACM Transactions on Networking ***26 **(2018), no. 6, 2501-2514. **DOI: **10.1109/TNET.2018.2869874.

· “On learning the cμ rule in single and parallel server networks,” Subhashini Krishnasamy, Ari Arapostathis, Ramesh Johari, and Sanjay Shakkottai, arXiv:1802.06723.

· “A counterexample to a nonlinear version of the Krein-Rutman theorem by R. Mahadevan,” Ari Arapostathis, *Nonlinear Analysis* **171C** (2018), 170-176. **DOI: **10.1016/j.na.2018.02.006.

· “Controlled equilibrium selection in stochastically perturbed dynamics,” Ari Arapostathis, Anup Biswas, and Vivek S. Borkar, *Annals of Probability* **46 **(2018), no. 5, 2749-2799. **DOI: **10.1214/17-AOP1238.

“Supplementary Material,” **DOI: **10.1214/17-AOP1238.

· “Infinite horizon average optimality of the N-network queueing model in the Halfin-Whitt regime,” Ari Arapostathis and Guodong Pang, *Mathematics of Operations Research* **43 **(2018), no. 3, 838-866. **DOI: **10.1287/moor.2017.0886.

· “Some new results on sample path optimality in ergodic control of diffusions,” Ari Arapostathis, *IEEE Transactions on Automatic Control* **62 **(2017), no. 10, 5351-5356. **DOI: **10.1109/TAC.2017.2664342.

· “Infinite horizon risk-sensitive control of diffusions without any blanket stability assumptions,” Ari Arapostathis and Anup Biswas, *Stochastic Processes and Their Applications* **128** (2018), no. 5, 1485-1524. **DOI:** 10.1016/j.spa.2017.08.001.

· “A correction to 'A relative value iteration algorithm for nondegenerate controlled diffusions',” Ari Arapostathis and Vivek S. Borkar, *SIAM Journal on Control and Optimization* **55** (2017), no. 3, 1711-1715. **DOI: **10.1137/16M110650X.

· “On solutions of mean field games with ergodic cost,” Ari Arapostathis, Anup Biswas, and Carroll Johnson, *Journal des Mathématiques Pures et Appliquées ***107 **(2017), no. 2, 205-251. **DOI:** 10.1016/j.matpur.2016.06.004.

· “The Dirichlet problem for stable-like operators and related probabilistic representations,” Ari Arapostathis, Anup Biswas, and Luis Caffarelli, *Communications in Partial Differential Equations* **41** (2016), no. 9, 1472-1511. **DOI:** 10.1080/03605302.2016.1207084.

· “Ergodic diffusion control of multiclass multi-pool networks in the Halfin–Whitt regime,” Ari Arapostathis and Guodong Pang, *Annals of Applied Probability* **26** (2016), no. 5, 3110-3153. **DOI: **10.1214/16-AAP1171.

· “Risk-sensitive control and an abstract Collatz–Wielandt formula,” Ari Arapostathis, Vivek S. Borkar, and K. Suresh Kumar, *J. Theoret. Probab.* **29** (2016), no. 4, 1458-1484. **DOI: **10.1007/s10959-015-0616-x.

· “Ergodic control of multi-class M/M/N+M queues in the Halfin-Whitt regime,” Ari Arapostathis, Anup Biswas, and Guodong Pang, *Annals of Applied Probability* **25** (2015), no. 6, 3511-3570. **DOI: **10.1214/14-AAP1081.

· “Resource allocation: realizing mean-variability-fairness tradeoffs,” Vinay Joseph, Gustavo de Veciana, and Ari Arapostathis, *IEEE Transactions on Automatic Control* **60** (2015), no. 1, 19-33. **DOI: **10.1109/TAC.2014.2332731.

· “Convergence of the relative value iteration for the ergodic control problem of nondegenerate diffusions under near-monotone costs,” Ari Arapostathis, Vivek S. Borkar, and K. Suresh Kumar, *SIAM Journal on Control and Optimization* **52** (2014), no. 1, 1-31. **DOI: **10.1137/130912918.

· “Relative value iteration for stochastic differential games,” Ari Arapostathis, Vivek S. Borkar, and K. Suresh Kumar. In Krivan V., Zaccur G. (eds) Advances in dynamic games, Annals of the International Society of Dynamic Games*,* vol. 13, pp. 3-27*,* Birkhäuser, Cham, 2013. **DOI: **10.1007/978-3-319-02690-9_1.

· “Aspiration learning in coordination games,” Georgios C. Chasparis, Ari Arapostathis, and Jeff S. Shamma, *SIAM Journal on Control and Optimization* **51** (2013), no. 1, 465-490. **DOI: **10.1137/110852462.

· “A relative value iteration algorithm for non-degenerate controlled diffusions,” Ari Arapostathis and Vivek S. Borkar, *SIAM Journal on Control and Optimization* **50** (2012), no. 4, 1886-1902. **DOI: **10.1137/110850529.

· *Ergodic Control of Diffusion Processes*, Ari Arapostathis, Vivek S. Borkar and Mrinal K. Ghosh, Encyclopedia of Mathematics and its Applications, vol. 143, Cambridge University Press, Cambridge, 2012.

· “On the policy iteration algorithm for non-degenerate controlled diffusions under the ergodic criterion,” Ari Arapostathis, *Optimization, control, and applications of stochastic systems*, 1-12, Systems Control Found. Appl., Birkhäuser/Springer, New York, 2012. **DOI: **10.1007/978-0-8176-8337-5_1.

· “On the adaptive control of a class of partially observed Markov decision processes,” Shun-Pin Hsu and Ari Arapostathis, *Journal of Mathematical Analysis and Applications* **380** (2011), no. 1, 1-9. **DOI: **10.1016/j.jmaa.2011.03.004.

· “Uniform recurrence properties of controlled diffusions and applications to optimal control,” Ari Arapostathis and Vivek S. Borkar, *SIAM Journal on Control and Optimization*** 48 **(2010), no. 7, 4181-4223. **DOI: **10.1137/090762464.

· “Necessary and sufficient conditions for state equivalence to a nonlinear discrete-time observer canonical form,” Hong-Gi Lee, Ari Arapostathis, and Steven I. Marcus, *IEEE Transactions on Automatic Control* **53 **(2008), no. 11, 2701-2707. **DOI: **10.1109/TAC.2008.2008321.

· “Optimal sensor querying: general Markovian and LQG models with controlled observations,” Wei Wu and Ari Arapostathis, *IEEE Transactions on Automatic Control* **53 **(2008), no. 6, 1392-1405. **DOI: **10.1109/TAC.2008.925817.

· “Stability and controllability of planar, conewise linear systems,” Ari Arapostathis and Mireille Broucke, *Systems & Control Letters* **56** (2007). no. 2, 150-158. **DOI: **10.1016/j.sysconle.2006.08.008.

· “Optimal power allocation for a time-varying wireless channel under heavy-traffic approximation,” Wei Wu, Ari Arapostathis, and Sanjay Shakkottai, *IEEE Transactions on Automatic Control* **51 **(2006), no. 4, 580-594. **DOI: **10.1109/TAC.2006.872838.

· “On the existence of stationary optimal policies for partially observed MDPs under the long-run average cost criterion,” Shun-Pin Hsu, Dong-Ming Chuang, and Ari Arapostathis, *Systems & Control Letters* **55 **(2006), no. 2, 165-173. **DOI: **10.1016/j.sysconle.2005.06.009.

· “Linearization of discrete-time systems via restricted dynamic feedback,” Hong-Gi Lee, Ari Arapostathis, and Steven I. Marcus, *IEEE Transactions on Automatic Control* **48 **(2003), no. 9, 1646-1650. **DOI: **10.1109/TAC.2003.817009.

· “Controlled Markov chains with safety upper bound,” Ari Arapostathis, Ratnesh Kumar, and Sekhar Tangirala, *IEEE Transactions on Automatic Control* **48 **(2003), no. 7, 1230-1234. **DOI: **10.1109/TAC.2003.814267.

· “Continuous selections of trajectories of hybrid systems,” Mireille Broucke and Ari Arapostathis, *Systems & Control Letters* **47** (2002), no. 2, 149-157. **DOI: **10.1016/S0167-6911(02)00185-8.

· “Continuous interpolation of solutions of Lipschitz inclusions,” Mireille Broucke and Ari Arapostathis, *Journal of Mathematical Analysis and Applications* **258** (2001), no. 2, 565-572. **DOI: **10.1006/jmaa.2000.7393.

· “On the controllability of a class of nonlinear stochastic systems,” Ari Arapostathis, Raju K. George, and Mrinal K. Ghosh, *Systems & Control Letters* **44** (2001), no. 1, 25-34. **DOI: **10.1016/S0167-6911(01)00123-2.

· “Harnack's inequality for cooperative weakly coupled elliptic systems,” Ari Arapostathis, Mrinal K. Ghosh, and Steven I. Marcus, *Communications in Partial Differential Equations* **24** (1999), no. 9-10, 1555-1571, 1999. **DOI: **10.1080/03605309908821475.