The paper presents some recently obtained results on the nonlinear filtering problem for infinite... more The paper presents some recently obtained results on the nonlinear filtering problem for infinite dimensional processes. The optimal filter is obtained as the unique solution of certain measure valued equations. Robustness properties — both pathwise and statistical — are given and a preliminary result shows consistency with the stochastic calculus theory. Applications to random fields and models of voltage potential in neurophysiology are briefly discussed.
In this paper, the problem of system identi cation is formulated as a problem in statistical lear... more In this paper, the problem of system identi cation is formulated as a problem in statistical learning theory. The main motivation for such a reformulation is that traditionally system identi cation theory provides asymptotic results, whereas statistical learning theory is devoted to the derivation of nite time estimates. If system identi cation is to be combined with robust control theory to develop a sound theory of indirect adaptive control, it is essential to have nite time estimates of the sort provided by statistical learning theory. As an illustration of the approach, a result is derived showing that in the case of systems with fading memory, it is possible to combine standard results in statistical learning theory (suitably modi ed to the present situation) with some fading memory arguments to obtain nite time estimates of the desired kind. In the case of linear systems, the results proved here are not overly conservative, but are more so in the case of nonlinear systems wher...
It is shown that the nonlinear filter is a measure-valued Markov process on a finitely additive p... more It is shown that the nonlinear filter is a measure-valued Markov process on a finitely additive probability space.
Abstract : Interacting Hilbert space valued stochastic differential equations are studied as an e... more Abstract : Interacting Hilbert space valued stochastic differential equations are studied as an extension of Funaki's model for random strings to a system of interacting strings. The martingale problem for the corresponding McKean-Vlasov equation is solved. Special results when H = L squared (G), G, a bounded domain in real numbers are obtained. Keywords: Mathematical equations/models, Differential equations.
In this chapter, we consider the stochastic differential equations of diffusion type and present ... more In this chapter, we consider the stochastic differential equations of diffusion type and present a result on the existence and uniqueness of solution. We also prove a version of the Feynman—Kac formula.
International Journal of Electrical Power & Energy Systems, 2010
In a competitive market scenario, consumers make payments for the consumption of electricity to r... more In a competitive market scenario, consumers make payments for the consumption of electricity to retailers at fixed tariff. The retailers buy power at the Market Clearing Price (MCP) in spot market and/or through bilateral contract at agreed upon price. Due to these different modes at buying and selling ends, the retailers are faced with an involved task of estimating their payoffs along with the risk-quantification. The methodology presented in this paper gives a range of bilateral quantity and associated price for a retailer to ensure risk-constrained payoff. The exercise is carried out with a single retailer in the market as well as for a case of competition amongst two retailers. Risk is quantified using Risk Adjusted Recovery on Capital (RAROC). The problem is evaluated to get a range of bilateral quantity to be quoted for a particular bilateral price at fixed tariff of loyal load and fixed value of switching load. This summary combined with risk-averseness of the retailer leads him to make a judicial choice about bilateral transactions such that it leads to a risk-constrained payoff.
The paper presents some recently obtained results on the nonlinear filtering problem for infinite... more The paper presents some recently obtained results on the nonlinear filtering problem for infinite dimensional processes. The optimal filter is obtained as the unique solution of certain measure valued equations. Robustness properties — both pathwise and statistical — are given and a preliminary result shows consistency with the stochastic calculus theory. Applications to random fields and models of voltage potential in neurophysiology are briefly discussed.
In this paper, the problem of system identi cation is formulated as a problem in statistical lear... more In this paper, the problem of system identi cation is formulated as a problem in statistical learning theory. The main motivation for such a reformulation is that traditionally system identi cation theory provides asymptotic results, whereas statistical learning theory is devoted to the derivation of nite time estimates. If system identi cation is to be combined with robust control theory to develop a sound theory of indirect adaptive control, it is essential to have nite time estimates of the sort provided by statistical learning theory. As an illustration of the approach, a result is derived showing that in the case of systems with fading memory, it is possible to combine standard results in statistical learning theory (suitably modi ed to the present situation) with some fading memory arguments to obtain nite time estimates of the desired kind. In the case of linear systems, the results proved here are not overly conservative, but are more so in the case of nonlinear systems wher...
It is shown that the nonlinear filter is a measure-valued Markov process on a finitely additive p... more It is shown that the nonlinear filter is a measure-valued Markov process on a finitely additive probability space.
Abstract : Interacting Hilbert space valued stochastic differential equations are studied as an e... more Abstract : Interacting Hilbert space valued stochastic differential equations are studied as an extension of Funaki's model for random strings to a system of interacting strings. The martingale problem for the corresponding McKean-Vlasov equation is solved. Special results when H = L squared (G), G, a bounded domain in real numbers are obtained. Keywords: Mathematical equations/models, Differential equations.
In this chapter, we consider the stochastic differential equations of diffusion type and present ... more In this chapter, we consider the stochastic differential equations of diffusion type and present a result on the existence and uniqueness of solution. We also prove a version of the Feynman—Kac formula.
International Journal of Electrical Power & Energy Systems, 2010
In a competitive market scenario, consumers make payments for the consumption of electricity to r... more In a competitive market scenario, consumers make payments for the consumption of electricity to retailers at fixed tariff. The retailers buy power at the Market Clearing Price (MCP) in spot market and/or through bilateral contract at agreed upon price. Due to these different modes at buying and selling ends, the retailers are faced with an involved task of estimating their payoffs along with the risk-quantification. The methodology presented in this paper gives a range of bilateral quantity and associated price for a retailer to ensure risk-constrained payoff. The exercise is carried out with a single retailer in the market as well as for a case of competition amongst two retailers. Risk is quantified using Risk Adjusted Recovery on Capital (RAROC). The problem is evaluated to get a range of bilateral quantity to be quoted for a particular bilateral price at fixed tariff of loyal load and fixed value of switching load. This summary combined with risk-averseness of the retailer leads him to make a judicial choice about bilateral transactions such that it leads to a risk-constrained payoff.
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Papers by Rajeeva Karandikar