### Browsing by Author "Ghosh, Mrinal K."

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Item Controlled Markov Processes on the Infinite Planning Horizon: Weighted and, Overtaking Cost Criteria(1993) Fernandez-Gaucherand, Emmanuel; Ghosh, Mrinal K.; Marcus, Steven I.; ISRStochastic control problems for controlled Markov processes models with an infinite planning horizon are considered, under some non-standard cost criteria. The classical discounted and average cost criteria can be viewed as complementary, in the sense that the former captures the short-time and the latter the long-time performance of the system. Thus, we study a cost criterion obtained as weighted combinations of these criteria, extending to a general state and control space framework several recent results by Feinberg and Shwartz, and by Krass et al. In addition, a functional characterization is given for overtaking optimal policies, for problems with countable state spaces and compact control spaces; our approach is based on qualitative properties of the optimality equation for problems with an average cost criterion.Item Discrete-Time Controlled Markov Processes with Average Cost Criterion: A Survey(1991) Arapostathis, Aristotle; Borkar, Vivek S.; Fernandez-Gaucherand, Emmanuel; Ghosh, Mrinal K.; Marcus, Steven I.; ISRThis work is a survey of the average cost control problem for discrete-time Markov processes. We have attempted to put together a comprehensive account of the considerable research on this problem over the past three decades. Our exposition ranges from finite to Borel state and action spaces and includes a variety of methodologies to find and characterize optimal policies. We have included a brief historical perspective of the research efforts in this area and have compiled a substantial yet not exhaustive bibliography. We have also identified several important questions which are still left open to investigation.Item Ergodic Control of Switching Diffusions(1992) Ghosh, Mrinal K.; Arapostathis, Aristotle; Marcus, Steven I.; ISRWe study the ergodic control problem of switching diffusions representing a typical hybrid system that arises in numerous applications such as fault tolerant control systems, flexible manufacturing systems, etc. Under certain conditions, we establish the existence of a stable Markov nonrandomized policy which is almost surely optimal for a pathwise longrun average cost criterion. We then study the corresponding Hamilton-Jacobi- Bellman (HJB) equation and establish the existence of a unique solution in a certain class. Using this, we characterize the optimal policy as a minimizing selector of the Hamiltonian associated with the HJB equations. We apply these results to a failure prone manufacturing system and show that the optimal production rate is of the hedging point type.Item Harnack's Inequality for Cooperative Weakly Coupled Elliptic Systems(1997) Arapostathis, Aristotle; Ghosh, Mrinal K.; Marcus, Steven I.; ISRWe consider cooperative, uniformly elliptic systems, with bounded coefficients and coupling in the zeroth-order terms. We establish two analogues of Harnack's inequality for this class of systems. A weak version is obtained under fairly general conditions, while imposing an irreducibility condition on the coupling coefficients we obtain a stronger version of the inequality. This irreducibility condition is also necessary for the existience of a Harnack constant for this class of systems. A Harnack inequality is also obtained for a class of superharmonic functions.Item A Note on an LQG Regulator with Markovian Switching and Pathwise Average Cost(1992) Ghosh, Mrinal K.; Arapostathis, Aristotle; Marcus, Steven I.; ISRWe study a linear system with a Markovian switching parameter perturbed by white noise. The cost function is quadratic. Under certain conditions, we find a linear feedback control which is almost surely optimal for the pathwise average cost over the infinite planning horizon.Item A Note on an LQG Regulator with Markovian Switching and Pathwise Average Cost(1994) Ghosh, Mrinal K.; Arapostathis, Aristotle; Marcus, Steven I.; ISRWe study a linear system with a Markovian switching parameter perturbed by white noise. The cost function is quadratic. Under certain conditions, we find a linear feedback control which is almost surely optimal for the pathwise average cost over the infinite planning horizon.Item Optimal Control of Switching Diffusions with Application to Flexible Manufacturing Systems(1991) Ghosh, Mrinal K.; Arapostathis, Aristotle; Marcus, Steven I.; ISRA Controlled switching diffusion model is developed to study the hierarchical control of flexible manufacturing systems. The existence of a homogeneous Markov nonrandomized optimal policy is established by a convex analytic method. Using the existence of such a policy, the existence of a unique solution in a certain class to the associated Hamilton-Jacobi-Bellman equations is established and the optimal policy is characterized as a minimizing selector of an appropriate Hamiltonian.Item Stochastic Differential Games with Multiple Modes(1995) Ghosh, Mrinal K.; Marcus, Steven I.; ISRWe have studied two-person stochastic differential games with multiple modes. For the zero-sum game we have established the existence of optimal strategies for both players. For the non- zero sum case we have proved the existence of a Nash equilibrium.